d Rewrite the mixed numbers as fractions. Remember that dividing by a fraction is the same as multiplying by its reciprocal.
A
a 1 19
B
b -13 310
C
c -14 1720
D
d -7 16
Practice makes perfect
a When we have an addition of two mixed numbers, we should rewrite the mixed numbers as sums. Note that 10 79 and 9 23 can be interpreted as the statements ten and seven ninths and nine and two thirds.
ccc
ten & and & seven ninths
10 & + & 7/9
nine & and & two thirds
9 & + & 2/3
Now we can evaluate the expression.
If we want to rewrite this fraction as a mixed number, we have to determine how many times 20 goes into 297. Since 20* 10=200, we know that it goes at least 10 times into 297. Let's continue from that.
&10* 20= 200
&11* 20= 220
&12* 20 = 240
&13* 20 = 260
&14* 20 = 280
&15* 20 = 300
As we can see, 20 goes at most 14 times into 297, which becomes the whole number part of our mixed number. To find the fraction part, we have to subtract 280 from 297.
297-280=17
The mixed number is - 14 1720.
d We solve the next exercise in the same way as in Part C, by first rewriting the mixed numbers as fractions.
If we want to rewrite this fraction as a mixed number, we have to determine how many times 6 goes into 43. Since 6* 5=30, we know that it goes at least 5 times into 43. Let's continue from that.
&5* 6= 30
&6* 6= 36
&7* 6= 42
&8* 6 = 48
As we can see, 30 goes at most 7 times into 43, which becomes the whole number part of our mixed number. To find the fraction part, we have to subtract 42 from 43.
43-42=1
The mixed number is - 7 16.
