This page offers Grade 7 math multiple choice questions on fractions and mixed numbers, designed to test both computation skills and conceptual understanding.
The questions range from basic fraction arithmetic to challenging order of operations and conversion problems, making them ideal for practice and review. Each problem includes a detailed, step-by-step solution to help students, parents, and teachers master the topic.
Note: Try to solve these questions without using a calculator to strengthen your arithmetic skills!
Find a fraction \(F\) with a denominator less than \(8\) such that:
\[ \dfrac{2}{8} + F = 1 \]
To find \(F\), isolate it by subtracting \( \dfrac{2}{8} \) from both sides:
\[ F = 1 - \dfrac{2}{8} \]
Find a common denominator. Rewrite 1 as \( \dfrac{8}{8} \):
\[ F = \dfrac{8}{8} - \dfrac{2}{8} = \dfrac{6}{8} \]
Reduce the fraction by dividing the numerator and denominator by 2:
\[ F = \dfrac{3}{4} \]
Correct Answer: A
Find two fractions \(F_1\) and \(F_2\) with a denominator of \(6\) such that:
\[ F_1 + F_2 = 1 \quad\text{and}\quad F_1 - F_2 = \dfrac{2}{3} \]
Write the equations with a common denominator of \(6\):
\[ F_1 + F_2 = 1 = \dfrac{6}{6} \]
\[ F_1 - F_2 = \dfrac{2}{3} = \dfrac{4}{6} \]
We are looking for two numerators that add up to 6 and have a difference of 4. Those numbers are 5 and 1.
\[ \dfrac{5}{6} + \dfrac{1}{6} = \dfrac{6}{6} \]
\[ \dfrac{5}{6} - \dfrac{1}{6} = \dfrac{4}{6} \]
Correct Answer: D
Which fraction is equivalent to \(16\%\)?
A percent is a number out of 100:
\[ 16\% = \dfrac{16}{100} \]
Reduce the fraction by dividing the numerator and denominator by their greatest common factor, 4:
\[ \dfrac{16 \div 4}{100 \div 4} = \dfrac{4}{25} \]
Correct Answer: B
Which fraction is equivalent to \( \dfrac{300}{1000} \)?
To simplify, divide both the numerator and the denominator by 100:
\[ \dfrac{300 \div 100}{1000 \div 100} = \dfrac{3}{10} \]
Correct Answer: C
Evaluate: \( \dfrac{1}{2} + \dfrac{1}{5} + \dfrac{1}{6} \)
Find the Least Common Multiple (LCM) of the denominators 2, 5, and 6.
Prime factorizations: \( 2 = 2 \), \( 5 = 5 \), \( 6 = 2 \times 3 \)
LCM \(= 2 \times 3 \times 5 = 30\)
Convert each fraction to have a denominator of 30:
\[ \dfrac{15}{30} + \dfrac{6}{30} + \dfrac{5}{30} = \dfrac{26}{30} \]
Reduce the fraction by dividing by 2:
\[ \dfrac{26 \div 2}{30 \div 2} = \dfrac{13}{15} \]
Correct Answer: B
Evaluate: \( 3\dfrac{3}{5} + 5\dfrac{1}{2} \)
Separate the whole numbers and the fractions:
\[ (3 + 5) + \left( \dfrac{3}{5} + \dfrac{1}{2} \right) \]
Find a common denominator (10) for the fractions:
\[ 8 + \left( \dfrac{6}{10} + \dfrac{5}{10} \right) = 8 + \dfrac{11}{10} \]
Convert the improper fraction to a mixed number: \( \dfrac{11}{10} = 1\dfrac{1}{10} \)
\[ 8 + 1\dfrac{1}{10} = 9\dfrac{1}{10} \]
Correct Answer: A
Evaluate: \( \dfrac{1}{7} \times 2\dfrac{2}{5} \)
First, convert the mixed number to an improper fraction:
\[ 2\dfrac{2}{5} = \dfrac{2 \times 5 + 2}{5} = \dfrac{12}{5} \]
Now multiply numerator by numerator, and denominator by denominator:
\[ \dfrac{1}{7} \times \dfrac{12}{5} = \dfrac{12}{35} \]
Correct Answer: C
Evaluate: \( \dfrac{1}{12} \times 0.2 \)
First, convert the decimal to a fraction in its simplest form:
\[ 0.2 = \dfrac{2}{10} = \dfrac{1}{5} \]
Multiply the fractions:
\[ \dfrac{1}{12} \times \dfrac{1}{5} = \dfrac{1}{60} \]
Correct Answer: D
Evaluate: \( \dfrac{2}{5} \div 6 \)
To divide by a whole number, multiply by its reciprocal (the reciprocal of 6 is \( \dfrac{1}{6} \)):
\[ \dfrac{2}{5} \times \dfrac{1}{6} = \dfrac{2}{30} \]
Simplify the fraction:
\[ \dfrac{2 \div 2}{30 \div 2} = \dfrac{1}{15} \]
Correct Answer: B
Evaluate: \( \dfrac{9}{7} + 2 \)
Write the whole number 2 as a fraction with a denominator of 7:
\[ 2 = \dfrac{14}{7} \]
Add the fractions:
\[ \dfrac{9}{7} + \dfrac{14}{7} = \dfrac{23}{7} \]
Convert the improper fraction to a mixed number:
\[ \dfrac{23}{7} = 3\dfrac{2}{7} \]
Correct Answer: A
Evaluate: \( 2\dfrac{1}{3} + \dfrac{4}{2} \)
First, simplify \( \dfrac{4}{2} \) to a whole number:
\[ \dfrac{4}{2} = 2 \]
Now add the whole number to the mixed number:
\[ 2\dfrac{1}{3} + 2 = 4\dfrac{1}{3} \]
Correct Answer: C
Evaluate: \( 3\dfrac{1}{5} \div 5 \)
Convert the mixed number to an improper fraction:
\[ 3\dfrac{1}{5} = \dfrac{16}{5} \]
To divide, multiply by the reciprocal of 5:
\[ \dfrac{16}{5} \times \dfrac{1}{5} = \dfrac{16}{25} \]
Correct Answer: C
Evaluate: \( \dfrac{1}{2} + 4\dfrac{1}{3} - 3\dfrac{2}{5} \)
Separate the whole numbers and the fractions:
\[ (4 - 3) + \left( \dfrac{1}{2} + \dfrac{1}{3} - \dfrac{2}{5} \right) \]
Find the Least Common Multiple for 2, 3, and 5, which is 30. Rewrite the fractions:
\[ 1 + \left( \dfrac{15}{30} + \dfrac{10}{30} - \dfrac{12}{30} \right) \]
Combine the numerators: \( 15 + 10 - 12 = 13 \)
\[ 1 + \dfrac{13}{30} = 1\dfrac{13}{30} \]
Correct Answer: A
Evaluate: \( \dfrac{5}{2} \div \dfrac{7}{2} - \dfrac{1}{5} \)
Following the order of operations (BEDMAS/PEMDAS), do the division first by multiplying by the reciprocal:
\[ \left(\dfrac{5}{2} \times \dfrac{2}{7}\right) - \dfrac{1}{5} \]
\[ \dfrac{5}{7} - \dfrac{1}{5} \]
Find a common denominator (35):
\[ \dfrac{25}{35} - \dfrac{7}{35} = \dfrac{18}{35} \]
Correct Answer: A
Evaluate: \( \left( 0.2 + \dfrac{1}{5} \right) \times \dfrac{2}{7} \)
First, resolve the parentheses. Convert the decimal \( 0.2 \) to the fraction \( \dfrac{1}{5} \):
\[ \left( \dfrac{1}{5} + \dfrac{1}{5} \right) \times \dfrac{2}{7} \]
\[ \dfrac{2}{5} \times \dfrac{2}{7} \]
Multiply numerators and denominators:
\[ \dfrac{4}{35} \]
Correct Answer: D
Evaluate: \( \left( 3\dfrac{1}{2} + \dfrac{3}{5} \right) \times \dfrac{1}{7} \)
Convert the mixed number to an improper fraction first: \( 3\dfrac{1}{2} = \dfrac{7}{2} \)
Find a common denominator (10) to add the fractions inside the parentheses:
\[ \left( \dfrac{35}{10} + \dfrac{6}{10} \right) \times \dfrac{1}{7} \]
\[ \dfrac{41}{10} \times \dfrac{1}{7} \]
Multiply:
\[ \dfrac{41}{70} \]
Correct Answer: B
Evaluate: \( \dfrac{40}{4000} \)
Simplify the fraction by dividing the numerator and denominator by 40:
\[ \dfrac{40 \div 40}{4000 \div 40} = \dfrac{1}{100} \]
Any fraction with a denominator of 100 represents a percentage:
\[ \dfrac{1}{100} = 1\% \]
Correct Answer: A
Evaluate: \( \left( \dfrac{1}{2} + \dfrac{2}{3} \right) \div 0.2 \)
First, add the fractions within the parentheses by finding a common denominator (6) and convert the decimal 0.2 to a fraction (\( \dfrac{1}{5} \)):
\[ \left( \dfrac{3}{6} + \dfrac{4}{6} \right) \div \dfrac{1}{5} \]
\[ \dfrac{7}{6} \div \dfrac{1}{5} \]
To divide by a fraction, multiply by its reciprocal:
\[ \dfrac{7}{6} \times \dfrac{5}{1} = \dfrac{35}{6} \]
Convert to a mixed number:
\[ \dfrac{35}{6} = 5\dfrac{5}{6} \]
Correct Answer: C
Order from least to greatest: \( 3\dfrac{4}{7},\quad 3\dfrac{3}{5},\quad 3\dfrac{1}{2},\quad 3\dfrac{11}{20} \)
To compare the numbers, find a common denominator for the fractional parts. The Least Common Multiple (LCM) of 7, 5, 2, and 20 is 140. Rewrite each fractional part:
\[ 3\dfrac{4}{7} = 3\dfrac{80}{140} \]
\[ 3\dfrac{3}{5} = 3\dfrac{84}{140} \]
\[ 3\dfrac{1}{2} = 3\dfrac{70}{140} \]
\[ 3\dfrac{11}{20} = 3\dfrac{77}{140} \]
By comparing the numerators (\( 70 < 77 < 80 < 84 \)), we can order the numbers from least to greatest:
\[ 3\dfrac{1}{2},\quad 3\dfrac{11}{20},\quad 3\dfrac{4}{7},\quad 3\dfrac{3}{5} \]
Correct Answer: A
Order from least to greatest: \( 2\dfrac{7}{8},\quad 2.66,\quad 262\%,\quad \dfrac{25}{8} \)
To compare these numbers, it is easiest to convert them all to decimal form:
\[ 2\dfrac{7}{8} = 2 + 0.875 = 2.875 \]
\[ 2.66 = 2.66 \]
\[ 262\% = \dfrac{262}{100} = 2.62 \]
\[ \dfrac{25}{8} = 3.125 \]
Comparing the decimal values (\( 2.62 < 2.66 < 2.875 < 3.125 \)), we can establish the order:
\[ 262\%,\quad 2.66,\quad 2\dfrac{7}{8},\quad \dfrac{25}{8} \]
Correct Answer: D