Practice Fraction practice: 6 questions with worked answers Six fraction practice questions, from easy to hard, with worked explanations. Pick an answer to check it, plus a common-denominator method.
These questions come from our SHSAT, TACHS and SSAT practice apps. For parents
Fractions show parts of a whole. Most fraction questions come down to a few skills: finding a common denominator, simplifying, and multiplying or dividing.
A common-denominator method for adding and subtracting
Find a common denominator. For 1/4 + 1/6, the smallest number both 4 and 6 divide into is 12.Rewrite each fraction. 1/4 = 3/12 and 1/6 = 2/12.Add or subtract the numerators. 3/12 + 2/12 = 5/12.Simplify if you can. 5/12 is already in simplest form.
To multiply fractions, multiply straight across: 2/3 × 3/5 = 6/15 = 2/5. To divide, flip the second fraction and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
The questions start easy and get harder. Try each one before you look at the explanation.
Practice questions Each question and explanation was reviewed by a person. Pick an answer to see if you're right.
Question 1 Nina picked 48 apples. She used
1 3 \frac{1}{3} 3 1 of the apples for pies and then used
3 4 \frac{3}{4} 4 3 of the REMAINING apples for applesauce. How many apples were left after that?
A 8 B 12 C 16 D 24 E 32
Pies used
1 3 × 48 = 16 \frac{1}{3} \times 48 = 16 3 1 × 48 = 16 apples, leaving
48 − 16 = 32 48 - 16 = 32 48 − 16 = 32 . Applesauce used
3 4 × 32 = 24 \frac{3}{4} \times 32 = 24 4 3 × 32 = 24 apples, leaving
32 − 24 = 8 32 - 24 = 8 32 − 24 = 8 . Sanity check by fractions of the whole:
2 3 \frac{2}{3} 3 2 remained after pies and
1 4 \frac{1}{4} 4 1 of that remained after applesauce, so
48 × 2 3 × 1 4 = 48 × 1 6 = 8 48 \times \frac{2}{3} \times \frac{1}{4} = 48 \times \frac{1}{6} = 8 48 × 3 2 × 4 1 = 48 × 6 1 = 8 apples, matching.
Question 2 What is the value of
3 4 1 2 + 1 8 \dfrac{\frac{3}{4}}{\frac{1}{2} + \frac{1}{8}} 2 1 + 8 1 4 3 ?
A 15 32 \dfrac{15}{32} 32 15 B 5 6 \dfrac{5}{6} 6 5 C 6 5 \dfrac{6}{5} 5 6 D 3 2 \dfrac{3}{2} 2 3 E 15 4 \dfrac{15}{4} 4 15
First simplify the denominator:
1 2 + 1 8 = 4 8 + 1 8 = 5 8 \frac{1}{2} + \frac{1}{8} = \frac{4}{8} + \frac{1}{8} = \frac{5}{8} 2 1 + 8 1 = 8 4 + 8 1 = 8 5 . Then divide:
3 4 ÷ 5 8 = 3 4 × 8 5 = 24 20 = 6 5 \frac{3}{4} \div \frac{5}{8} = \frac{3}{4} \times \frac{8}{5} = \frac{24}{20} = \frac{6}{5} 4 3 ÷ 8 5 = 4 3 × 5 8 = 20 24 = 5 6 . Sanity check with decimals:
0.75 ÷ 0.625 = 1.2 0.75 \div 0.625 = 1.2 0.75 ÷ 0.625 = 1.2 , and
6 5 = 1.2 \frac{6}{5} = 1.2 5 6 = 1.2 , so the value is
6 5 \frac{6}{5} 5 6 .
Question 3 What is the value of
− 5 6 − ( − 3 4 ) + ( − 1 2 ) -\dfrac{5}{6}-\left(-\dfrac{3}{4}\right)+\left(-\dfrac{1}{2}\right) − 6 5 − ( − 4 3 ) + ( − 2 1 ) ?
A − 25 12 -\dfrac{25}{12} − 12 25 B − 7 12 -\dfrac{7}{12} − 12 7 C 5 12 \dfrac{5}{12} 12 5 D − 1 12 -\dfrac{1}{12} − 12 1
Rewrite subtracting a negative as adding, and adding a negative as subtracting:
− 5 6 + 3 4 − 1 2 -\frac{5}{6}+\frac{3}{4}-\frac{1}{2} − 6 5 + 4 3 − 2 1 . Over a common denominator of 12:
− 10 12 + 9 12 − 6 12 = − 10 + 9 − 6 12 = − 7 12 -\frac{10}{12}+\frac{9}{12}-\frac{6}{12}=\frac{-10+9-6}{12}=-\frac{7}{12} − 12 10 + 12 9 − 12 6 = 12 − 10 + 9 − 6 = − 12 7 .
Question 4 A wooden plank is
7 1 6 7\tfrac{1}{6} 7 6 1 feet long. A piece
2 5 8 2\tfrac{5}{8} 2 8 5 feet long is cut off. How long is the remaining plank, in feet?
A 4 11 24 4\tfrac{11}{24} 4 24 11 B 4 13 24 4\tfrac{13}{24} 4 24 13 C 4 5 6 4\tfrac{5}{6} 4 6 5 D 5 E 5 11 24 5\tfrac{11}{24} 5 24 11
Rewrite with denominator 24:
7 1 6 = 7 4 24 7\tfrac{1}{6}=7\tfrac{4}{24} 7 6 1 = 7 24 4 and
2 5 8 = 2 15 24 2\tfrac{5}{8}=2\tfrac{15}{24} 2 8 5 = 2 24 15 . Since
4 24 < 15 24 \tfrac{4}{24}<\tfrac{15}{24} 24 4 < 24 15 , regroup
7 4 24 = 6 28 24 7\tfrac{4}{24}=6\tfrac{28}{24} 7 24 4 = 6 24 28 . Then
6 28 24 − 2 15 24 = 4 13 24 6\tfrac{28}{24}-2\tfrac{15}{24}=4\tfrac{13}{24} 6 24 28 − 2 24 15 = 4 24 13 feet. (Check:
43 6 − 21 8 = 172 24 − 63 24 = 109 24 = 4 13 24 \tfrac{43}{6}-\tfrac{21}{8}=\tfrac{172}{24}-\tfrac{63}{24}=\tfrac{109}{24}=4\tfrac{13}{24} 6 43 − 8 21 = 24 172 − 24 63 = 24 109 = 4 24 13 .)
Question 5 A carpenter starts with a board
8 1 4 8\frac{1}{4} 8 4 1 feet long and cuts off a piece
2 5 6 2\frac{5}{6} 2 6 5 feet long. How many feet of board are left?
A 5 1 4 5\frac{1}{4} 5 4 1 B 5 5 12 5\frac{5}{12} 5 12 5 C 6 6 6 D 6 7 12 6\frac{7}{12} 6 12 7 E 11 1 12 11\frac{1}{12} 11 12 1
Rewrite with a common denominator of 12:
8 1 4 = 8 3 12 8\frac{1}{4}=8\frac{3}{12} 8 4 1 = 8 12 3 and
2 5 6 = 2 10 12 2\frac{5}{6}=2\frac{10}{12} 2 6 5 = 2 12 10 . Since
3 12 < 10 12 \frac{3}{12}<\frac{10}{12} 12 3 < 12 10 , regroup one whole:
8 3 12 = 7 15 12 8\frac{3}{12}=7\frac{15}{12} 8 12 3 = 7 12 15 . Then
7 15 12 − 2 10 12 = 5 5 12 7\frac{15}{12}-2\frac{10}{12}=5\frac{5}{12} 7 12 15 − 2 12 10 = 5 12 5 . Check by decimals:
8.25 − 2.833 … ≈ 5.417 = 5 5 12 8.25-2.833\ldots\approx5.417=5\frac{5}{12} 8.25 − 2.833 … ≈ 5.417 = 5 12 5 , which is
5 5 12 5\frac{5}{12} 5 12 5 .
Question 6 A community garden plot is planted in stages. First,
2 5 \tfrac{2}{5} 5 2 of the plot is planted with tomatoes. Then
3 8 \tfrac{3}{8} 8 3 of the land that still remains is planted with peppers. The last
30 30 30 square yards are left bare. How many square yards is the entire plot?
A 48 B 50 C 75 D 80
After tomatoes, the remaining fraction is
1 − 2 5 = 3 5 1-\tfrac{2}{5}=\tfrac{3}{5} 1 − 5 2 = 5 3 . Peppers take
3 8 \tfrac{3}{8} 8 3 of that:
3 8 ⋅ 3 5 = 9 40 \tfrac{3}{8}\cdot\tfrac{3}{5}=\tfrac{9}{40} 8 3 ⋅ 5 3 = 40 9 . The bare fraction is
3 5 − 9 40 = 24 40 − 9 40 = 15 40 = 3 8 \tfrac{3}{5}-\tfrac{9}{40}=\tfrac{24}{40}-\tfrac{9}{40}=\tfrac{15}{40}=\tfrac{3}{8} 5 3 − 40 9 = 40 24 − 40 9 = 40 15 = 8 3 . So
3 8 \tfrac{3}{8} 8 3 of the plot equals 30 square yards, giving a plot of
30 ÷ 3 8 = 80 30\div\tfrac{3}{8}=80 30 ÷ 8 3 = 80 square yards. The option 75 comes from equating 30 with the tomato fraction; 50 from treating 30 as the full remainder
3 5 \tfrac{3}{5} 5 3 ; 48 from using the planted fraction
5 8 \tfrac{5}{8} 8 5 .
For parents
These practice questions come from our SHSAT, TACHS and SSAT practice apps. Each app has more than 1,200 practice questions, every one with a worked explanation.
Checked against official sources. How we make this site Wednesday, September 30, 2026