I need help please

Question

David was 40 3/4 inches tall in first grade. He is 6 7/12 tall in sixth grade. About how many inches taller is David in sixth grade then he was in first grade?

Answer 1

40 3/8 - 6 7/12 can't be subtracted until we've created equivalent fractions with common denominators.

The common multiple of 8 and 12 is 24. 3/8 x 3/3 = 9/24 7/12 x 2/2 = 14/24

Now we have 40 9/24 - 6 14/24 but there's still another step because 9/24 < 14/24

40 9/24 is 39 + 24/24 + 9/24 or 39 33/24 We've borrowed 1, or 24/24 from the 40.

Now we can subtract: 39 33/24 - 6 14/24 = 33 19/24.

This method is an alternative to the conversion to improper fractions used by Peter F. It's a little involved, but doesn't involve the larger numbers.

Answer 2

Hello CoolKat,

The first thing you need to do is convert your two mixed numbers into improper fractions by multiplying the denominator of each mixed number by its respective whole number in the given mixed number and that adding the separate products to their mixed number's respective numerator.

In other words:

40 3/8 as an improper fraction equals 323/8 (40 x 8 = 320; 320 + 3 = 323).

6 7/12 as an improper fractions equals 79/12 (6 x 12 = 72; 72 + 7 = 79).

Now we have to find the difference between 323/8 and 79/12 by subtracting the two fractions in that order.

But first we must find a common denominator. Between the numeric values of the original two denominators of 8 and 12 in the improper fractions written above: the common denominator in this case is 24 since both 8 and 12 can be multiplied evenly into 24.

So with 24 as our common denominator, we need to multiply 323 x 3 since we multiplied 8 x 3 to get 24 in the first improper fraction. Our new improper fraction therefore becomes 669/24.

Now we multiply 79 x 2 since we multiplied 12 x 2 to get 24 in the second improper fraction. Our new improper fraction therefore becomes 158/24.

Subtract: 669/24 - 158/24.

Our initial answer is: 559/24.

We can convert that improper fraction into a mixed number by dividing the whole numerator 559 by the whole denominator 24--resulting in 23 7/24.

And voila!

David is approximately 23 inches taller in sixth grade than he was in first grade.