SAT Math: Ratios, Rates & Proportions

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<h1>Ratios, Rates, and Proportions: Free SAT Math Lesson</h1>

"Ratios, rates, proportional relationships, and units" is the first skill listed in College Board's official Problem-Solving and Data Analysis domain, and it's one of the most consistently tested topics on the Digital SAT. This free, complete lesson covers everything: what a ratio is and how to simplify one, the crucial difference between a part-to-part ratio and a part-to-whole ratio, the standard rate formulas for unit price, gas mileage, speed, and density, dividing a quantity according to a given ratio, the definition of a proportion with extremes and means, the cross-products property, checking whether two ratios form a proportion, solving proportions for a variable, and setting up proportions from word problems. Each idea is followed by a fully worked example, and then a set of original practice problems with instant feedback. Everything here is free, and you can keep practicing afterward with the full SAT Math Question Bank linked below.

</p>

<a class="cta-btn cta-primary" href="https://theschoolofmathematics.com/quiz/sat-ratios-rates-proportional-relationships-quiz-1">Practice Ratios, Rates & Proportions Free</a>

<a class="cta-btn cta-secondary" href="https://theschoolofmathematics.com/quiz/course/SAT-Math-Qbank">Explore the Full SAT Math Qbank</a>

</div>

<h2>What's covered in this lesson</h2>

<ol>

<li><a href="#ratios">What Is a Ratio?</a></li>

<li><a href="#part-to-part">Part-to-Part vs. Part-to-Whole Ratios</a></li>

<li><a href="#rates">Rates and Unit Rates</a></li>

<li><a href="#dividing">Dividing a Quantity in a Given Ratio</a></li>

<li><a href="#definition">What Is a Proportion?</a></li>

<li><a href="#checking">Checking Whether Ratios Form a Proportion</a></li>

<li><a href="#solving">Solving Proportions for a Variable</a></li>

<li><a href="#word-problems">Setting Up Proportions from Word Problems</a></li>

<li><a href="#mistakes">Common Mistakes to Avoid</a></li>

<li><a href="#faq">Frequently Asked Questions</a></li>

</ol>

</nav>

<h2 id="ratios">1. What Is a Ratio?</h2>

<p>A <strong>ratio</strong> is a comparison of two quantities by division. The ratio of a to b can be written three different ways: a to b, a : b, or <span class="frac"><span class="num">a</span><span class="den">b</span></span>. If two quantities are in the ratio a to b, the actual amounts can be represented as ax and bx, where x is a positive number, this lets you scale the ratio up or down while keeping the same proportion.</p>

<p><strong>Worked Example:</strong> The ratio of red marbles to blue marbles in a bag is 5 : 3. If there are 15 red marbles, how many blue marbles are there?</p>

<p>Since 15 red marbles corresponds to 5 parts, each part represents 15 ÷ 5 = 3 marbles. Blue marbles, at 3 parts, total 3 × 3 = 9.</p>

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<p class="prompt">1. A recipe calls for 2 cups of flour for every 3 cups of sugar. Which ratio represents flour to sugar?</p>

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<p><span class="label">Explanation:</span> "Flour to sugar" means flour is listed first, so the ratio is 2 : 3.</p>

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<p class="prompt">2. Simplify the ratio 18 to 24 to lowest terms.</p>

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<p><span class="label">Explanation:</span> The greatest common factor of 18 and 24 is 6. Dividing both by 6 gives 3 : 4.</p>

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<p class="prompt">3. The ratio of red marbles to blue marbles in a bag is 5 : 3. If there are 15 red marbles, how many blue marbles are there?</p>

</div>

<p><span class="label">Explanation:</span> This is the worked example above: 15 red marbles means each of the 5 parts equals 3, so blue marbles (3 parts) total 9.</p>

</div>

<p class="prompt">4. Two numbers are in the ratio 4 : 7. If the smaller number is 4x, which expression represents the larger number?</p>

</div>

<p><span class="label">Explanation:</span> If the two quantities are in the ratio 4 : 7, they can be represented as 4x and 7x for the same value of x. Since the smaller number is 4x, the larger is 7x.</p>

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<h2 id="part-to-part">2. Part-to-Part vs. Part-to-Whole Ratios</h2>

<p>This distinction trips up more students than any other ratio concept, and it's worth slowing down for. A ratio like "boys to girls is 3 : 5" is a <strong>part-to-part</strong> ratio, it compares one part of a group to another part. But the fraction of the group that is boys is <strong>not</strong> <span class="frac"><span class="num">3</span><span class="den">5</span></span>, it's <span class="frac"><span class="num">3</span><span class="den">8</span></span>, since the total group has 3 + 5 = 8 parts. Comparing a part to the entire total is a <strong>part-to-whole</strong> ratio, and mixing the two up is one of the most common ratio errors on the SAT.</p>

<p><strong>Worked Example:</strong> In a class, the ratio of boys to girls is 3 : 5. If there are 24 students total, how many are boys?</p>

<p>The ratio has 3 + 5 = 8 total parts. Each part represents 24 ÷ 8 = 3 students. Boys, at 3 parts, total 3 × 3 = 9 students.</p>

</div>

<p class="prompt">1. A fruit basket has apples and oranges in the ratio 2 : 3. What fraction of the fruit is apples?</p>

</div>

<p><span class="label">Explanation:</span> The total number of parts is 2 + 3 = 5. Apples make up 2 of those 5 parts, so the fraction is <span class="frac"><span class="num">2</span><span class="den">5</span></span>, not <span class="frac"><span class="num">2</span><span class="den">3</span></span>.</p>

</div>

<p class="prompt">2. In a bag of 40 marbles, red and blue marbles are in the ratio 3 : 5. How many red marbles are there?</p>

</div>

<p><span class="label">Explanation:</span> The ratio has 3 + 5 = 8 total parts. Each part represents 40 ÷ 8 = 5 marbles. Red marbles, at 3 parts, total 3 × 5 = 15.</p>

</div>

<p class="prompt">3. The ratio of cats to dogs at a shelter is 4 : 7. What is the ratio of cats to the total number of animals?</p>

</div>

<p><span class="label">Explanation:</span> The total number of parts is 4 + 7 = 11. The ratio of cats (a part) to the total (the whole) is 4 : 11.</p>

</div>

<h2 id="rates">3. Rates and Unit Rates</h2>

<p>A <strong>rate</strong> is a ratio of two measurements with different units, like $2.59 per gallon or 60 miles per hour. A <strong>unit rate</strong> is a rate with a denominator of 1. Several common unit rates appear repeatedly on the SAT:</p>

<tr><th>Quantity</th><th>Formula</th></tr>

<tr><td>Unit price</td><td><span class="frac"><span class="num">Price of package</span><span class="den">Number of units in the package</span></span></td></tr>

<tr><td>Gas mileage</td><td><span class="frac"><span class="num">Number of miles traveled</span><span class="den">Number of gallons of gas used</span></span></td></tr>

<tr><td>Speed</td><td><span class="frac"><span class="num">Number of miles traveled</span><span class="den">Number of hours</span></span></td></tr>

<tr><td>Density</td><td><span class="frac"><span class="num">Mass</span><span class="den">Volume</span></span></td></tr>

</table>

<p><strong>Worked Example:</strong> A car travels 276 miles on 8 gallons of gas. What is the car's gas mileage?</p>

<p class="step-math"><span class="frac"><span class="num">276 mi</span><span class="den">8 gal</span></span> = 34.5 miles per gallon</p>

</div>

<p class="prompt">1. A 15-ounce box of cereal costs $4.50. What is the unit price, per ounce?</p>

</div>

<p><span class="label">Explanation:</span> Unit price = <span class="frac"><span class="num">$4.50</span><span class="den">15 oz</span></span> = $0.30 per ounce.</p>

</div>

<p class="prompt">2. A car travels 276 miles on 8 gallons of gas. What is the car's gas mileage?</p>

<button class="option-btn" data-correct="true" onclick="checkAnswer(this,'pc-2',true)">A) 34.5 miles per gallon</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pc-2',false)">B) 8 miles per gallon</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pc-2',false)">C) 34 miles per gallon</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pc-2',false)">D) 276 miles per gallon</button>

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<p><span class="label">Explanation:</span> This is the worked example above: 276 ÷ 8 = 34.5 miles per gallon.</p>

</div>

<p class="prompt">3. A driver traveled 202<span class="frac"><span class="num">1</span><span class="den">2</span></span> miles in 4<span class="frac"><span class="num">1</span><span class="den">2</span></span> hours. What was his speed, in miles per hour?</p>

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<p><span class="label">Explanation:</span> Speed = <span class="frac"><span class="num">202.5 mi</span><span class="den">4.5 hr</span></span> = 45 miles per hour.</p>

</div>

<p class="prompt">4. A volume of 25 cm³ of a metal has a mass of 197.5 grams. What is the metal's density?</p>

</div>

<p><span class="label">Explanation:</span> Density = <span class="frac"><span class="num">mass</span><span class="den">volume</span></span> = <span class="frac"><span class="num">197.5 g</span><span class="den">25 cm³</span></span> = 7.9 g/cm³.</p>

</div>

<p class="prompt">5. Which is the better unit price: a 12-pack of soda for $5.40, or an 18-pack for $7.65?</p>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pc-5',false)">C) They are the same price per can</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pc-5',false)">D) Cannot be determined</button>

</div>

<p><span class="label">Explanation:</span> The 12-pack costs $5.40 ÷ 12 = $0.45 per can. The 18-pack costs $7.65 ÷ 18 = $0.425 per can. Since $0.425 < $0.45, the 18-pack is the better deal.</p>

</div>

<h2 id="dividing">4. Dividing a Quantity in a Given Ratio</h2>

<p>A common SAT setup gives a total amount, like a sum of money, a total angle measure, or a total profit, split among parts in a given ratio. Represent each part using the ax, bx, ... notation, set their sum equal to the total, and solve for x.</p>

<p><strong>Worked Example:</strong> The three angles of a triangle are in the ratio 2 : 3 : 4. What is the measure of each angle?</p>

<p>The angle sum of a triangle is 180°.</p>

<p>The three angles measure 2(20) = 40°, 3(20) = 60°, and 4(20) = 80°.</p>

</div>

<p class="prompt">1. The measures of the three angles of a triangle are in the ratio 1 : 2 : 3. What is the measure of the largest angle?</p>

</div>

<p><span class="label">Explanation:</span> x + 2x + 3x = 180, so 6x = 180, and x = 30. The largest angle is 3(30) = 90°.</p>

</div>

<p class="prompt">2. A sum of $600 is divided between two people in the ratio 2 : 3. How much does each person receive?</p>

</div>

<p><span class="label">Explanation:</span> 2x + 3x = 600, so 5x = 600, and x = 120. The two shares are 2(120) = $240 and 3(120) = $360.</p>

</div>

<p class="prompt">3. Three business partners divide a profit of $84,000 in the ratio 3 : 4 : 5. What is the largest share?</p>

</div>

<p><span class="label">Explanation:</span> 3x + 4x + 5x = 84,000, so 12x = 84,000, and x = 7,000. The largest share is 5(7,000) = $35,000.</p>

</div>

<p class="prompt">4. A rectangle's length and width are in the ratio 5 : 2. If the perimeter is 84 units, what is the length?</p>

</div>

<p><span class="label">Explanation:</span> Perimeter = 2(length + width) = 84, so length + width = 42. With length and width in the ratio 5 : 2, there are 7 total parts, so each part is 42 ÷ 7 = 6. The length, at 5 parts, is 5(6) = 30.</p>

</div>

<h2 id="definition">5. What Is a Proportion?</h2>

<p>A <strong>proportion</strong> is an equation stating that two ratios are equal. The proportion <span class="frac"><span class="num">a</span><span class="den">b</span></span> = <span class="frac"><span class="num">c</span><span class="den">d</span></span> is read "a is to b as c is to d." The numbers a and d are called the <strong>extremes</strong> of the proportion, and the numbers b and c are called the <strong>means</strong>.</p>

<text x="85" y="12" font-size="11" fill="#4285f4">extremes</text>

<text x="80" y="90" font-size="11" fill="#ea4335">means</text>

</svg>

</div>

<p>In a proportion, the product of the extremes equals the product of the means, this is called the <strong>cross-products property</strong>. If <span class="frac"><span class="num">a</span><span class="den">b</span></span> = <span class="frac"><span class="num">c</span><span class="den">d</span></span>, then ad = bc. This single property is what makes proportions so useful, it turns a comparison of fractions into a simple equation you can solve.</p>

<p class="prompt">1. In the proportion <span class="frac"><span class="num">3</span><span class="den">7</span></span> = <span class="frac"><span class="num">9</span><span class="den">21</span></span>, which two numbers are the means?</p>

</div>

<p><span class="label">Explanation:</span> In <span class="frac"><span class="num">a</span><span class="den">b</span></span> = <span class="frac"><span class="num">c</span><span class="den">d</span></span>, the means are b and c, the two "inner" numbers. Here, a = 3, b = 7, c = 9, d = 21, so the means are 7 and 9.</p>

</div>

<p class="prompt">2. If <span class="frac"><span class="num">a</span><span class="den">b</span></span> = <span class="frac"><span class="num">c</span><span class="den">d</span></span>, which equation represents the cross products?</p>

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<p><span class="label">Explanation:</span> The cross-products property states that the product of the extremes (a and d) equals the product of the means (b and c): ad = bc.</p>

</div>

<p class="prompt">3. In the proportion <span class="frac"><span class="num">a</span><span class="den">b</span></span> = <span class="frac"><span class="num">c</span><span class="den">d</span></span>, which two quantities are called the extremes?</p>

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<p><span class="label">Explanation:</span> The extremes are the two "outer" numbers in the proportion, a and d.</p>

</div>

<h2 id="checking">6. Checking Whether Ratios Form a Proportion</h2>

<p>To determine whether two ratios form a proportion, find the cross products. If the cross products are equal, the ratios form a proportion. If not, they don't.</p>

<p><strong>Worked Example:</strong> Determine whether <span class="frac"><span class="num">0.6</span><span class="den">2.4</span></span> and <span class="frac"><span class="num">1.5</span><span class="den">6</span></span> form a proportion.</p>

<p>The cross products are equal, so the ratios form a proportion.</p>

</div>

<p class="prompt">1. Do the ratios <span class="frac"><span class="num">8</span><span class="den">12</span></span> and <span class="frac"><span class="num">6</span><span class="den">9</span></span> form a proportion?</p>

<button class="option-btn" data-correct="true" onclick="checkAnswer(this,'pf-1',true)">A) Yes, since the cross products are equal</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-1',false)">B) No, since the cross products are unequal</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-1',false)">C) Yes, since both ratios equal 1</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-1',false)">D) No, since the numerators differ</button>

</div>

<p><span class="label">Explanation:</span> 8 × 9 = 72 and 12 × 6 = 72. The cross products are equal, so the ratios form a proportion.</p>

</div>

<p class="prompt">2. Do the ratios <span class="frac"><span class="num">14</span><span class="den">35</span></span> and <span class="frac"><span class="num">4</span><span class="den">9</span></span> form a proportion?</p>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-2',false)">A) Yes, since 126 = 140</button>

<button class="option-btn" data-correct="true" onclick="checkAnswer(this,'pf-2',true)">B) No, since 126 ≠ 140</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-2',false)">C) Yes, since both simplify to <span class="frac"><span class="num">2</span><span class="den">5</span></span></button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-2',false)">D) No, since the denominators are prime</button>

</div>

<p><span class="label">Explanation:</span> 14 × 9 = 126 and 35 × 4 = 140. Since 126 ≠ 140, the ratios do not form a proportion.</p>

</div>

<p class="prompt">3. Do the ratios <span class="frac"><span class="num">0.75</span><span class="den">3</span></span> and <span class="frac"><span class="num">2.5</span><span class="den">10</span></span> form a proportion?</p>

<button class="option-btn" data-correct="true" onclick="checkAnswer(this,'pf-3',true)">A) Yes, since the cross products are both 7.5</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-3',false)">B) No, since one ratio involves a decimal</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-3',false)">C) No, since the cross products are unequal</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'pf-3',false)">D) Cannot be determined without a calculator</button>

</div>

<p><span class="label">Explanation:</span> 0.75 × 10 = 7.5 and 3 × 2.5 = 7.5. The cross products are equal, so the ratios form a proportion.</p>

</div>

<p class="prompt">4. Which pair of ratios does NOT form a proportion?</p>

</div>

<p><span class="label">Explanation:</span> For <span class="frac"><span class="num">5</span><span class="den">8</span></span> and <span class="frac"><span class="num">10</span><span class="den">15</span></span>: 5 × 15 = 75, but 8 × 10 = 80. Since these are unequal, this pair does not form a proportion. Every other pair has equal cross products.</p>

</div>

<h2 id="solving">7. Solving Proportions for a Variable</h2>

<p>To solve a proportion that contains a variable, cross-multiply to clear the fractions, then solve the resulting equation using the same steps you'd use for any linear equation.</p>

<p><strong>Worked Example:</strong> Solve <span class="frac"><span class="num">5</span><span class="den">8</span></span> = <span class="frac"><span class="num">15</span><span class="den">x + 2</span></span>.</p>

<p class="step-math">5(x + 2) = 8(15)   (Cross products)</p>

<p class="step-math">5x + 10 = 120   (Distribute)</p>

<p class="step-math">5x = 110   (Subtract 10 from each side)</p>

<p class="step-math">x = 22   (Divide each side by 5)</p>

</div>

<p class="prompt">1. Solve: <span class="frac"><span class="num">3</span><span class="den">5</span></span> = <span class="frac"><span class="num">x</span><span class="den">20</span></span></p>

</div>

<p><span class="label">Explanation:</span> Cross-multiply: 3(20) = 5x, so 60 = 5x, and x = 12.</p>

</div>

<p class="prompt">2. Solve: <span class="frac"><span class="num">7</span><span class="den">x</span></span> = <span class="frac"><span class="num">21</span><span class="den">9</span></span></p>

</div>

<p><span class="label">Explanation:</span> Cross-multiply: 7(9) = 21x, so 63 = 21x, and x = 3.</p>

</div>

<p class="prompt">3. Solve: <span class="frac"><span class="num">4</span><span class="den">x − 3</span></span> = <span class="frac"><span class="num">8</span><span class="den">10</span></span></p>

</div>

<p><span class="label">Explanation:</span> Cross-multiply: 4(10) = 8(x − 3), so 40 = 8x − 24. Add 24 to each side: 64 = 8x, and x = 8.</p>

</div>

<p class="prompt">4. Solve: <span class="frac"><span class="num">x + 1</span><span class="den">6</span></span> = <span class="frac"><span class="num">5</span><span class="den">3</span></span></p>

</div>

<p><span class="label">Explanation:</span> Cross-multiply: 3(x + 1) = 6(5), so 3x + 3 = 30. Subtract 3: 3x = 27, and x = 9.</p>

</div>

<p class="prompt">5. Solve: <span class="frac"><span class="num">9</span><span class="den">2x</span></span> = <span class="frac"><span class="num">3</span><span class="den">8</span></span></p>

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<p><span class="label">Explanation:</span> Cross-multiply: 9(8) = 3(2x), so 72 = 6x, and x = 12.</p>

</div>

<h2 id="word-problems">8. Setting Up Proportions from Word Problems</h2>

<p>Many SAT word problems give you one known ratio and ask you to scale it up or down. The cleanest way to set these up is to write two ratios with matching units in matching positions, top and bottom, then cross-multiply and solve.</p>

<p><strong>Worked Example:</strong> A car requires 6 gallons of gasoline to travel 132 miles. How much gasoline, to the nearest gallon, will it need for a 350-mile trip?</p>

<p>Let g be the number of gallons needed.</p>

<p class="step-math">miles → <span class="frac"><span class="num">132</span><span class="den">6</span></span> = <span class="frac"><span class="num">350</span><span class="den">g</span></span> ← miles</p>

<p class="step-math">gallons →                 ← gallons</p>

<p>Rounded to the nearest gallon, the car needs about 16 gallons.</p>

</div>

<p class="prompt">1. A recipe uses 3 eggs for every 8 cups of flour. How many eggs are needed for 24 cups of flour?</p>

</div>

<p><span class="label">Explanation:</span> <span class="frac"><span class="num">3</span><span class="den">8</span></span> = <span class="frac"><span class="num">x</span><span class="den">24</span></span>. Cross-multiply: 8x = 3(24) = 72, so x = 9.</p>

</div>

<p class="prompt">2. A map has a scale of 1 inch = 15 miles. If two cities are 4.5 inches apart on the map, what is the actual distance between them?</p>

<button class="option-btn" data-correct="true" onclick="checkAnswer(this,'ph-2',true)">A) 67.5 miles</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'ph-2',false)">B) 60 miles</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'ph-2',false)">C) 19.5 miles</button>

<button class="option-btn" data-correct="false" onclick="checkAnswer(this,'ph-2',false)">D) 3.33 miles</button>

</div>

<p><span class="label">Explanation:</span> <span class="frac"><span class="num">1</span><span class="den">15</span></span> = <span class="frac"><span class="num">4.5</span><span class="den">x</span></span>. Cross-multiply: x = 15(4.5) = 67.5 miles.</p>

</div>

<p class="prompt">3. A factory produces 450 units in 5 hours. At this rate, how many units will it produce in 8 hours?</p>

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<p><span class="label">Explanation:</span> <span class="frac"><span class="num">450</span><span class="den">5</span></span> = <span class="frac"><span class="num">x</span><span class="den">8</span></span>. Cross-multiply: 5x = 450(8) = 3,600, so x = 720.</p>

</div>

<p class="prompt">4. A car requires 7 gallons of gasoline to travel 154 miles. How much gasoline, to the nearest gallon, will it need for a 400-mile trip?</p>

</div>

<p><span class="label">Explanation:</span> <span class="frac"><span class="num">154</span><span class="den">7</span></span> = <span class="frac"><span class="num">400</span><span class="den">g</span></span>. Cross-multiply: 154g = 7(400) = 2,800, so g = <span class="frac"><span class="num">2,800</span><span class="den">154</span></span> ≈ 18.18, which rounds to 18 gallons.</p>

</div>

<h2 id="mistakes">Common Mistakes to Avoid</h2>

<li><strong>Treating a part-to-part ratio as a part-to-whole fraction.</strong> If a ratio is "3 to 5," the fraction of the total that the first quantity represents is <span class="frac"><span class="num">3</span><span class="den">8</span></span>, not <span class="frac"><span class="num">3</span><span class="den">5</span></span>. Always add the parts of the ratio to find the whole before computing a part-to-whole fraction.</li>

<li><strong>Writing a ratio in the wrong order.</strong> "The ratio of x to y" always means x first, y second. Reading a word problem quickly can lead to flipping the order by accident.</li>

<li><strong>Confusing which quantity goes in the numerator of a rate.</strong> Gas mileage is miles per gallon (miles on top), not gallons per mile. Reversing a rate's numerator and denominator is a common and costly error.</li>

<li><strong>Skipping the step of finding x when dividing a quantity in a ratio.</strong> Don't distribute the total directly across the ratio numbers, always solve for the value of one part first (x), then multiply back to find each share.</li>

<li><strong>Mismatching units when setting up a proportion.</strong> Whatever unit is on top of the first ratio must be on top of the second ratio too. Writing miles over gallons on one side and gallons over miles on the other will give a completely wrong answer.</li>

<li><strong>Forgetting to distribute when a cross product creates a binomial.</strong> If cross-multiplying gives you something like 5(x + 2), you must distribute the 5 across both terms before continuing to solve.</li>

<li><strong>Rounding too early in a multi-step word problem.</strong> Keep exact values (or extra decimal places) through the intermediate steps, and only round at the very end, exactly as the question asks.</li>

</ul>

<h2 id="faq">Frequently Asked Questions</h2>

<h3>Is a ratio the same thing as a fraction?</h3>

<p>They're closely related but not identical. A ratio compares two quantities and can describe a part-to-part relationship, like 3 boys for every 5 girls. A fraction specifically represents a part out of a whole. Every part-to-whole ratio can be written as a fraction, but a part-to-part ratio cannot be read directly as a fraction of the total without first finding the sum of the parts.</p>

</div>

<h3>Is a proportion just a ratio written differently?</h3>

<p>A proportion is an equation that sets two ratios equal to each other, so it builds on ratios rather than being a different concept entirely. Once you can express a relationship as a ratio, writing a proportion just means saying that ratio stays the same as the quantities scale up or down.</p>

</div>

<h3>Should I use cross-multiplication or a different method to solve a proportion?</h3>

<p>Cross-multiplication is the fastest and most reliable method for a proportion with a variable. It's really just a shortcut for multiplying both sides by a common denominator to clear the fractions, so it always gives the same result.</p>

</div>

<h3>Where can I practice more problems like these?</h3>

<p>The <a href="https://theschoolofmathematics.com/quiz/sat-ratios-rates-proportional-relationships-quiz-1">Ratios, Rates, and Proportional Relationships quizzes</a> in the SAT Math Question Bank include additional original problems on this topic, along with quizzes covering every other Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry skill on the Digital SAT.</p>

</div>

<a class="cta-btn cta-primary" href="https://theschoolofmathematics.com/quiz/sat-ratios-rates-proportional-relationships-quiz-1">Practice Ratios, Rates & Proportions Free</a>

<a class="cta-btn cta-secondary" href="https://theschoolofmathematics.com/quiz/course/SAT-Math-Qbank">Explore the Full SAT Math Qbank</a>

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