NCERT Class 7 Ganita Prakash 1 Chapter 08 Working with Fractions PDF Download

Chapter 8: Working with Fractions

8.1 Multiplication of Fractions

Aaron walks 3 kilometres in 1 hour. How far can he walk in 5 hours?

This is a simple question. We know that to find the distance, we need to find the product of 5 and 3, i.e., we multiply 5 and 3.

Distance covered in 1 hour = 3 km.

Therefore,

Distance covered in 5 hours
= \( 5 \times 3 \) km
= \( 3 + 3 + 3 + 3 + 3 \) km
= 15 km.

Aaron's pet tortoise walks at a much slower pace. It can walk only \( \frac{1}{4} \) kilometre in 1 hour. How far can it walk in 3 hours?

Here, the distance covered in an hour is a fraction. This does not matter. The total distance covered is calculated in the same way, as multiplication.

Distance covered in 1 hour = \( \frac{1}{4} \) km.

[Figure: Number line showing distance in 1 hour and distance in 3 hours, See in your textbook]

Therefore, distance covered in 3 hours = \( 3 \times \frac{1}{4} \) km
= \( \frac{1}{4} + \frac{1}{4} + \frac{1}{4} \) km
= \( \frac{3}{4} \) km.

The tortoise can walk \( \frac{3}{4} \) km in 3 hours.

Let us consider a case where the time spent walking is a fraction of an hour.

We saw that Aaron can walk 3 kilometres in 1 hour. How far can he walk in \( \frac{1}{5} \) hours?

We continue to calculate the total distance covered through multiplication.

Distance covered in \( \frac{1}{5} \) hours = \( \frac{1}{5} \times 3 \) km.

[Figure: Number line showing distance in 1 hour and distance in 1/5 hour, See in your textbook]

Finding the product:

Distance covered in 1 hour = 3 km.

In \( \frac{1}{5} \) hours, distance covered is equal to the length we get by dividing 3 km into 5 equal parts, which is \( \frac{3}{5} \) km.

This tells us that \( \frac{1}{5} \times 3 = \frac{3}{5} \).

Teacher's Note

When you multiply a whole number by a fraction with numerator 1, like \( \frac{1}{5} \times 3 \), think of it as dividing the whole number into that many equal parts. You are taking 1 out of 5 parts, so divide 3 by 5 to get \( \frac{3}{5} \). This is why \( \frac{1}{5} \times 3 = \frac{3}{5} \).

How far can Aaron walk in \( \frac{2}{5} \) hours?

Once again, we have -
Distance covered = \( \frac{2}{5} \times 3 \) km.

[Figure: Number line showing distance in 1 hour, distance in 1/5 hour, and distance in 2/5 hour, See in your textbook]

Finding the product:

1. We can first find the distance covered in \( \frac{1}{5} \) hours.
2. Since, the duration \( \frac{2}{5} \) is twice \( \frac{1}{5} \), we multiply this distance by 2 to get the total distance covered.

Here is the calculation.

Distance covered in 1 hour = 3 km.

1. Distance covered in \( \frac{1}{5} \) hour
   = The length we get by dividing 3 km in 5 equal parts
   = \( \frac{3}{5} \) km.
2. Multiplying this distance by 2, we get
   \( 2 \times \frac{3}{5} = \frac{6}{5} \) km.

From this we can see that
\( \frac{2}{5} \times 3 = \frac{6}{5} \).

Discussion

We did this multiplication as follows:

• First, we divided the multiplicand, 3, by the denominator of the multiplier, 5, to get \( \frac{3}{5} \).

Teacher's Note

Notice the pattern: when you multiply a fraction by a whole number, you multiply the numerator by that whole number and keep the denominator the same. So \( \frac{2}{5} \times 3 = \frac{2 \times 3}{5} = \frac{6}{5} \). This shortcut saves time compared to finding \( \frac{1}{5} \) first and then multiplying by 2.

Key Points

• To find the total distance or quantity when you have a fractional rate, multiply the rate by the number of time units, just as you would with whole numbers.
• When multiplying a fraction with numerator 1 by a whole number, divide the whole number by the denominator to get the result.
• When multiplying any fraction by a whole number, multiply the numerator by that whole number and keep the denominator unchanged.

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