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Fraction Multiplied by a Whole Number

🎓 Class 7 Mathematics CBSE Theory Ch 8 — Working with Fractions ⏱ ~35 min
🌐 Language: [gtranslate]

This MCQ module is based on: Fraction Multiplied by a Whole Number

This mathematics assessment will be based on: Fraction Multiplied by a Whole Number
Targeting Class 7 level in Fractions, with Basic difficulty.

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Chapter 8 — Working with Fractions

8.1 Multiplication of Fractions

Aaron walks 3 km in 1 hour. How far will he walk in 5 hours? A quick repeated addition gives \(3+3+3+3+3=15\) km, or equivalently \(5\times 3=15\) km.

Now consider Aaron's pet tortoise, which walks only \(\frac14\) km in 1 hour. In 5 hours the tortoise walks:

\(\frac14 + \frac14 + \frac14 + \frac14 + \frac14 = \frac{5}{4}\) km, i.e. \(5\times\frac14 = \frac{5\times 1}{4} = \frac54\) km.

0 1/4 2/4 3/4 4/4 5/4 Five hops of 1/4 each
Five jumps of \(\tfrac14\) km on the number line reach \(\tfrac54\) km.

Multiplying a Whole Number by a Fraction

How far does Aaron walk in \(\frac12\) hour, given that he covers 3 km in one hour? Half the distance of 1 hour is \(\frac12\times 3 = \frac32\) km.

In general, \(\dfrac{a}{b}\times n = \dfrac{a\times n}{b}\). We multiply the whole number with the numerator, keeping the denominator unchanged.

Rule
\(\displaystyle n\times\frac{a}{b} = \frac{n\times a}{b} = \frac{a}{b}\times n.\) The result may turn out larger or smaller than \(n\) depending on whether \(a/b\) is greater or less than 1.

Worked Examples

Example 1. \(3\times \frac{1}{4} = \frac{3}{4}\).

Example 2. \(5\times \frac{2}{3} = \frac{10}{3} = 3\tfrac13\).

Example 3. \(\frac{2}{5}\times 3 = \frac{6}{5}=1\tfrac15\).

= 2/5 (×1) = 2/5 (×2) = 2/5 (×3)
Area model: three copies of \(\tfrac25\) give \(\tfrac{6}{5}\).

Figure it Out

Q1. Compute: (a) \(4\times\frac25\), (b) \(7\times\frac38\), (c) \(\frac{11}{4}\times 2\), (d) \(\frac{12}{5}\times 6\).
(a) \(\tfrac{8}{5}=1\tfrac35\); (b) \(\tfrac{21}{8}=2\tfrac58\); (c) \(\tfrac{22}{4}=\tfrac{11}{2}=5\tfrac12\); (d) \(\tfrac{72}{5}=14\tfrac25\).
Q2. Convert each improper fraction to a mixed number: (a) \(7\times\tfrac23\), (b) \(4\times\tfrac15\), (c) \(\tfrac96\times 2\), (d) \(\tfrac{12}{5}\times 6\).
(a) \(\tfrac{14}{3}=4\tfrac23\); (b) \(\tfrac{4}{5}\); (c) \(\tfrac{18}{6}=3\); (d) \(\tfrac{72}{5}=14\tfrac25\).
Q3. Aaron's tortoise walks \(\tfrac14\) km/h. How far in (a) 2 h, (b) 6 h, (c) \(\tfrac12\) h?
(a) \(2\times\tfrac14=\tfrac12\) km; (b) \(6\times\tfrac14=\tfrac32\) km; (c) \(\tfrac12\times\tfrac14=\tfrac18\) km.
Activity: Paper-Strip Multiplication
Materials: 10 rectangular paper strips of equal length, scissors, ruler.
  1. Fold each strip into 4 equal parts and shade one part on each. Each shaded part is \(\tfrac14\) of a strip.
  2. Place three strips end-to-end; count the total shaded length.
  3. Verify that \(3\times \tfrac14 = \tfrac34\) of a strip.
  4. Repeat with strips folded in 5 equal parts, shading 2; find \(4\times\tfrac25\).
\(4\times\tfrac25 = \tfrac85 = 1\tfrac35\) — total shaded equals one full strip plus \(\tfrac35\) of another.

Competency-Based Questions

Scenario: A bakery packs laddoos into boxes. Each box holds \(\tfrac34\) kg of laddoos. An order needs 8 boxes.
Q1. What is the total weight of laddoos in the 8 boxes?
L3 Apply
\(8\times\tfrac34 = \tfrac{24}{4} = 6\) kg.
Q2. The owner doubles the filling (each box now \(1\tfrac12\) kg). Analyse by how much the total grows.
L4 Analyse
New total \(8\times\tfrac32=12\) kg. Increase = \(12-6=6\) kg — exactly doubled.
Q3. Evaluate: "Multiplying any whole number by a proper fraction gives a smaller product." True or false, justify.
L5 Evaluate
True (for positive whole numbers > 0). A proper fraction is less than 1, so \(n\times\text{(<1)}
Q4. Create a word problem that results in the calculation \(5\times\tfrac27\).
L6 Create
Sample: "A marathon runner drinks \(\tfrac27\) L of water every 5 km. How much does she drink after running 25 km (five times)?" Answer: \(5\times\tfrac27=\tfrac{10}{7}\) L.

Assertion–Reason Questions

A: \(6\times\tfrac34 = \tfrac92\).
R: To multiply a whole number by a fraction, multiply the whole number by the numerator and keep the denominator.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
(a) — \(6\times 3/4 = 18/4 = 9/2\). R explains A.
A: \(5\times\tfrac12 > 5\).
R: Multiplying by a proper fraction decreases the value.
(a) Both true, R explains A.
(b) Both true, R doesn't explain A.
(c) A true, R false.
(d) A false, R true.
(d) — A is false: \(5\times\tfrac12 = 2.5 < 5\). R is true.

Frequently Asked Questions

What does 'fraction times a whole number' mean?
It means repeated addition of the fraction. For example, 3 times 2/5 is 2/5 plus 2/5 plus 2/5, which equals 6/5 or 1 1/5.
How do you multiply 4 by 3/7?
Multiply 4 by the numerator 3 to get 12 and keep the denominator 7, giving 12/7. Convert to mixed form: 1 5/7.
Does multiplication always make a number bigger?
Not always. Multiplying by a proper fraction (less than 1) gives a smaller result, while multiplying by an improper fraction or whole number greater than 1 gives a larger result.
How do you multiply a mixed fraction by a whole number?
Convert the mixed fraction to an improper fraction, multiply the numerator by the whole number, and simplify. Finally, convert back to a mixed fraction if appropriate.
Why do we simplify after multiplication?
Simplifying gives the answer in its standard form, making it easier to compare with other fractions and matching NCERT expectations for final answers.
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