If we want to rewrite this fraction as a mixed number, we have to determine how many times 65 goes into 168. Since 65* 1=65, we know that it goes at least 1 time into 65. Let's continue from that.
&1* 65= 65
&2* 65= 130
&3* 65 = 195
As we can see, 65 goes at most 2 times into 168, which becomes the whole number part of our mixed number. To find the fraction part, we have to subtract 130 from 168.
168-130=38
The mixed number is 2 3865.
b We solve the next exercise in the same way as in Part A, by first rewriting the mixed numbers as fractions.
Let's rewrite this as a mixed number. Since 8* 30=240, we know that 8 goes at least 30 times into 297. Let's continue from that.
8* 30= 240
8* 31= 248
8* 32= 256
8* 33 = 264
8* 34 = 272
8* 35 = 280
8* 36 = 288
8* 37 = 296
8* 38 = 304
As we can see, 8 goes 37 times into 297 which becomes the whole number part of our mixed number. To find the fraction part, we have to subtract 296 from 297.
297-296=1
The mixed number is 37 18.
c When we have a subtraction of two mixed numbers, we should rewrite the mixed numbers as sums. Note that 3 58 and 1 12 can be interpreted as the statements three and five eights and one and one half.
ccc
three & and & five eights
3 & + & 5/8
one & and & one half
1 & + & 1/2Now we can evaluate the expression.
Let's rewrite this as a mixed number. Since 3* 5=15, we know that 3 goes at least 5 times into 19. Let's continue from that.
3* 5= 15
3* 6= 18
3* 7 = 21
As we can see, 3 goes 6 times into 19, which becomes the whole number part of our mixed number. To find the fraction part we have to subtract 18 from 19.
19-18=1
The mixed number is - 6 13.
