Video: Solving Word Problems by Multiplying Fractions by Whole Numbers

Dalia had 70 LE to spend at the market. She spent 2/5 of her money on meat and 1/5 of her money on vegetables. How much did she spend in total?

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Video Transcript

Dalia had 70 Egyptian pounds to spend at the market. She spent two-fifths of her money on meat and one-fifth of her money on vegetables. How much did she spend in total?

Let’s begin by identifying the key information in this question. We’re told that the total amount of money that Dalia has to spend is 70 Egyptian pounds. We’re also told that the fractions of the money that she spends on meat and vegetables are two-fifths and one-fifth. We’re then asked to work out how much she spent in total.

First, let’s work out the total fraction of her money that Dalia has spent. We need to add together two-fifths and one-fifth. As these fractions have a common denominator of five, then the denominator of the result will be five and we can add the numerators together. Two-fifths plus one-fifth is equal to three-fifths.

To work out how much Dalia spent in total, we need to calculate three-fifths of 70. When we see the word “of” being used in a calculation involving fractions, it means that we can multiply. Three-fifths of 70 means three-fifths multiplied by 70. So the calculation that we need to perform is a fraction three-fifths multiplied by an integer 70.

Perhaps, the most common way to approach this is to think of the integer 70 as a fraction: 70 over one. We can then remember that the rules for multiplying two fractions together tell us that we need to multiply the numerators and multiply the denominators. The result will be three multiplied by 70 over five multiplied by one.

We can actually simplify this fraction before we perform the multiplications, as both five and 70 have a common factor of five. Five divided by five is one and 70 divided by five is 14. So we can cancel the two numbers down. We could also have performed this cross-cancellation at an earlier stage.

The calculation is now three multiplied by 14 over one multiplied by one. Three multiplied by 14 is 42 and one multiplied by one is one. So we have the fraction 42 over one. As the denominator of this fraction is one, the whole fraction is just equivalent to 42.

The amount of money that Dalia spent in total is 42 Egyptian pounds.

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