Let's solve each problem step by step. The task is to
find the missing whole number that makes each multiplication equation true.
We are multiplying a fraction by a whole number, and we need to find that whole number.
---
Problem 1:
$$
\frac{5}{2} \times \boxed{} = \frac{25}{2}
$$
Let the missing number be $ x $.
So:
$$
\frac{5}{2} \times x = \frac{25}{2}
$$
To solve for $ x $, divide both sides by $ \frac{5}{2} $:
$$
x = \frac{25}{2} \div \frac{5}{2} = \frac{25}{2} \times \frac{2}{5} = \frac{50}{10} = 5
$$
✔ Answer: 5
---
Problem 2:
$$
\frac{2}{11} \times \boxed{} = \frac{18}{11}
$$
Let $ x $ be the missing number:
$$
\frac{2}{11} \times x = \frac{18}{11}
$$
Solve:
$$
x = \frac{18}{11} \div \frac{2}{11} = \frac{18}{11} \times \frac{11}{2} = \frac{198}{22} = 9
$$
✔ Answer: 9
---
Problem 3:
$$
\frac{1}{5} \times \boxed{} = \frac{3}{5}
$$
Let $ x $ be the missing number:
$$
\frac{1}{5} \times x = \frac{3}{5}
$$
Solve:
$$
x = \frac{3}{5} \div \frac{1}{5} = \frac{3}{5} \times \frac{5}{1} = 3
$$
✔ Answer: 3
---
Problem 4:
$$
\frac{13}{4} \times \boxed{} = \frac{91}{4}
$$
Let $ x $ be the missing number:
$$
\frac{13}{4} \times x = \frac{91}{4}
$$
Solve:
$$
x = \frac{91}{4} \div \frac{13}{4} = \frac{91}{4} \times \frac{4}{13} = \frac{364}{52} = 7
$$
✔ Answer: 7
---
Problem 5:
$$
\frac{7}{2} \times \boxed{} = \frac{49}{2}
$$
Let $ x $ be the missing number:
$$
\frac{7}{2} \times x = \frac{49}{2}
$$
Solve:
$$
x = \frac{49}{2} \div \frac{7}{2} = \frac{49}{2} \times \frac{2}{7} = \frac{98}{14} = 7
$$
✔ Answer: 7
---
Problem 6:
$$
\frac{6}{7} \times \boxed{} = \frac{54}{7}
$$
Let $ x $ be the missing number:
$$
\frac{6}{7} \times x = \frac{54}{7}
$$
Solve:
$$
x = \frac{54}{7} \div \frac{6}{7} = \frac{54}{7} \times \frac{7}{6} = \frac{378}{42} = 9
$$
✔ Answer: 9
---
✔ Final Answers:
1. $ \frac{5}{2} \times \boxed{5} = \frac{25}{2} $
2. $ \frac{2}{11} \times \boxed{9} = \frac{18}{11} $
3. $ \frac{1}{5} \times \boxed{3} = \frac{3}{5} $
4. $ \frac{13}{4} \times \boxed{7} = \frac{91}{4} $
5. $ \frac{7}{2} \times \boxed{7} = \frac{49}{2} $
6. $ \frac{6}{7} \times \boxed{9} = \frac{54}{7} $
---
🔍 Explanation:
To multiply a fraction by a whole number:
- Multiply the numerator of the fraction by the whole number.
- Keep the denominator the same.
But here, we're given the result and need to find the missing whole number.
So, we use:
> $$
> \text{Whole number} = \frac{\text{Result}}{\text{Fraction}}
> $$
Which is equivalent to multiplying the result by the reciprocal of the fraction.
This method works because:
$$
\frac{a}{b} \times x = \frac{c}{b} \Rightarrow x = \frac{c}{b} \div \frac{a}{b} = \frac{c}{a}
$$
Notice in all cases, the denominators are the same, so you can just divide the numerators.
For example:
- $ \frac{25}{2} \div \frac{5}{2} = \frac{25}{5} = 5 $
That’s a shortcut! If the denominators are the same, just divide the numerators.
---
✔ Summary: Use division or the shortcut (same denominator → divide numerators) to find the missing whole number.
All answers are whole numbers as expected.
Parent Tip: Review the logic above to help your child master the concept of multiplying whole numbers and fractions worksheet.
