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Fractions, decimals, and operations — ACT practice questions

Fractions, decimals, and operations on the ACT Mathematics test covers converting between fractions and decimals, comparing their values, and adding, subtracting, multiplying, and dividing them in short word problems and in number-only items. A student must find how much of a planned quantity remains after some of it is used, list mixed fractions and decimals from least to greatest, and write a part of a whole as a simplified fraction. Questions are multiple choice, with options that look like mixed numbers, decimals, or unsimplified fractions. Common traps include ranking by digit appearance, skipping a conversion before operating, and selecting the used amount instead of what is left.

  • Section: Mathematics 45 questions on the paper
  • 51 practice questions in the app

Sample questions

Question 1

An online poll received responses from 45 of the 1,4401{,}440 invited participants. What fraction of the invited participants responded?

  1. A148\dfrac{1}{48}
  2. B132\dfrac{1}{32}
  3. C124\dfrac{1}{24}
  4. D332\dfrac{3}{32}
Show answer

Answer: B — 132\dfrac{1}{32}

451,440=132\dfrac{45}{1{,}440}=\dfrac{1}{32}.

Question 2

Leona plans a 5165\dfrac16-mile route and completes 23\dfrac23 mile before breakfast. After completing another 34\dfrac34 mile later, how many miles of the planned route remain?

  1. A2512\dfrac{25}{12}
  2. B196\dfrac{19}{6}
  3. C154\dfrac{15}{4}
  4. D174\dfrac{17}{4}
Show answer

Answer: C — 154\dfrac{15}{4}

The completed distance is 23+34=1712\dfrac23+\dfrac34=\dfrac{17}{12} mile. Subtracting from 516=62125\dfrac16=\dfrac{62}{12} leaves 4512=154\dfrac{45}{12}=\dfrac{15}{4} miles.

Question 3

Which of the following lists the values 35\dfrac{3}{5}, 0.58, 0.605, and 712\dfrac{7}{12} in order from least to greatest?

  1. A0.58, 712, 35, 0.6050.58,\ \dfrac7{12},\ \dfrac35,\ 0.605
  2. B712, 0.58, 35, 0.605\dfrac7{12},\ 0.58,\ \dfrac35,\ 0.605
  3. C0.58, 35, 712, 0.6050.58,\ \dfrac35,\ \dfrac7{12},\ 0.605
  4. D0.605, 35, 712, 0.580.605,\ \dfrac35,\ \dfrac7{12},\ 0.58
Show answer

Answer: A — 0.58, 712, 35, 0.6050.58,\ \dfrac7{12},\ \dfrac35,\ 0.605

The fractions are 712≈0.5833\dfrac7{12}\approx0.5833 and 35=0.6\dfrac35=0.6. Thus, the correct order is 0.58<712<35<0.6050.58<\dfrac7{12}<\dfrac35<0.605.

Practice 51 Fractions, decimals, and operations questions in the app

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