- Multiply and Divide Fractions
- Home
- Product of a Unit Fraction and a Whole Number
- Product of a Fraction and a Whole Number: Problem Type 1
- Introduction to Fraction Multiplication
- Fraction Multiplication
- Product of a Fraction and a Whole Number Problem Type 2
- Determining if a Quantity is Increased or Decreased When Multiplied by a Fraction
- Modeling Multiplication of Proper Fractions
- Multiplication of 3 Fractions
- Word Problem Involving Fractions and Multiplication
- The Reciprocal of a Number
- Division Involving a Whole Number and a Fraction
- Fraction Division
- Fact Families for Multiplication and Division of Fractions
- Modeling Division of a Whole Number by a Fraction
- Word Problem Involving Fractions and Division

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- UPSC IAS Exams Notes
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The product of a number multiplied by a fraction is not always smaller than the original number. A number multiplied by a fraction can also give an equal number or a number greater than the original number.

Multiply 2 × $\frac{1}{3}$ and determine if 2 is decreased/increased/same on multiplying by $\frac{1}{3}$

**Step 1:**

2 × $\frac{1}{3}$ = $\frac{2}{1}$ × $\frac{1}{3}$ = $\frac{(2 × 1)}{(1 × 3)}$ = $\frac{2}{3}$

**Step 2:**

Comparing 2 and $\frac{2}{3}$

$\frac{2}{3}$ (the product) < 2 (the original number)

**Step 3:**

So, in this case the number is decreased when multiplied by a proper fraction.

Multiply 3 × $\frac{4}{4}$. and determine if 3 is decreased/increased/same on multiplying by $\frac{4}{4}$.

**Step 1:**

3 × $\frac{4}{4}$ = $\frac{3}{1}$ × $\frac{4}{4}$ = $\frac{(3 × 4)}{(1 × 4)}$ = $\frac{12}{4}$ = $\frac{3}{1}$

**Step 2:**

Comparing 3 and $\frac{3}{1}$

$\frac{3}{1}$(the product) = 3 (the original number)

**Step 3:**

So, in this case the number is same (neither decreased or increased) when multiplied by a fraction which is equal to 1.

Multiply 3 × $\frac{3}{2}$. and determine if 2 is decreased/increased/same on multiplying by $\frac{3}{2}$.

**Step 1:**

2 × $\frac{3}{2}$ = $\frac{2}{1}$ × $\frac{3}{2}$ = $\frac{(2 × 3)}{(1 × 2)}$ = $\frac{6}{2}$ = $\frac{3}{1}$ = 3

**Step 2:**

Comparing 2 and 3

3 (the product) > 2 (the original number)

**Step 3:**

So, in this case the number is increased when multiplied by an improper fraction.

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