Solutions and explanations to grade 5 fractions questions are presented.
Use any whole number n to write 1 as a fraction as follows:
n=1, 1=11
n=2, 1=22
n=11, 1=1111
and so on
NOTE that we cannot write 1=00.
NOTE that a fraction cannot have a denominator equal to zero.
Any whole number n may be written as a reduced fraction as follows: n1 Hence 5 may be written as 51
When adding fractions, it is important to have a common denominator. In this case, both fractions have a denominator of 4, so we can add the numerators directly. The sum of the numerators gives us the numerator of the resulting fraction. The denominator remains the same. So, the resulting fraction is 14+24=1+24=34
When subtracting fractions, it is important to have a common denominator. In this case, both fractions have a denominator of 7, so we can subtract the numerators directly. The difference between the numerators gives us the numerator of the resulting fraction. The denominator remains the same. So, the resulting fraction is 47−27=4−27=27
15+23=
To add the fractions, we need to follow these steps:
Step 1: Find a common denominator.
In this case, the denominators are different (5 and 3). To find a common denominator, we can multiply the denominators together:
5×3=15
Step 2: Rewrite the fractions so that they have the same denominator.
To make the denominators equal to 15, we need to scale the fractions accordingly.
We multiply the numerator and denominator of
15 by 3, and the numerator and denominator of 23 by 5:
15=15×33=315
23=23×55=1015
Now, both fractions have the same denominator of 15.
Step 3: Add the adjusted fractions. We can now add the adjusted fractions:
315+1015=3+1013=1315
Therefore, the sum of
15+23=1315
To add the mixed numbers 312 and 513, we can follow these steps:
Step 1: Analyze the whole parts of 312 and 513.
The whole part of 312 is 3, and the whole part of 513 is 5.
Step 2: Analyze the fractions: The fraction part of 312 is 12 and the fraction part of 513 is 13
Step 3: Add the whole parts.
We add the whole parts together: 3+5=8
Step 4: Add the fraction parts: 12+13
Step 5: Find a common denominator.
To add the fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 2 and 3 is 6.
Step 6: Multiply (adjust) the fractions to have a common denominator of 6:
12=12×33=36
13=13×22=26
Step 7: Add the fractions.
We add the adjusted fractions together:
12+13=36+26=56
Step 8: Put all together.
312+513=(3+5)+12+13=8+56
The total time for Julia to be ready for school is
12 hour+14 hour=(12+14) hour
Write fractions with the same denominator
12+14=12×22+14=24+14=34 hour.
It is easier to compare fractions if they are written with the same denominator
A)
52 and 25 with same denominator become
52=52×55=2510
25=25×22=410
Therefore 52 and 25 are not equivalent
B)
Write 43 with denominator 8 as follows
43=43×22=86
Therefore 43 and 86 are equivalent
The fractions in parts C) and D) already have the same denominators and are not equivalent.
Conclusion: Fractions 4/3 and 8/6 are equivalent because when written with common denominator both denominators and numerators are equal.
To subtract the mixed numbers 523 and 312, we follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
523=5+23=533+23=153+23=173
and
312=3+12=322+12=62+12=72,
Step 2: Find a common denominator to the 2 fractions: The denominators of the fractions are 3 and 2, which are different. To find a common denominator, we multiply them: 3×2=6.
Step 2: Write the fractions with a common denominator.
173=173×22=346
72=72×33=216,
Step 4: Subtract the adjusted fractions.
523−312=346−216=136
Step 5: Reduce (if possible) and convert the improper fraction back to a mixed number (if desired).
136 cannot be reduced but can be written as a mixed number
136=12+16=126+16=216
John ate more than Billy and the difference is given by
123−114=(1−1)+(23−14)=(23−14)
Write fractions with the same denominator
23=23×44=812
14=14×33=312
The difference is
123−114=812−312=512
John ate 512 of a pizza more than Billy.
To divide two fractions, you multiply the first one by the multiplicative inverse of the second
The multiplicative inverse of fraction ab is the fraction ba
Change the division of two fractions into a multiplication as follows
52÷34=52×43=5×42×3=206
The result is an improper fraction and may be written as a mixed number as follows:
206=18+26=186+26=3+26
The fraction 26 may be reduced by dividing its numerator and denominator by 2
26=2÷26÷2=13
Finally
52÷34=313
To divide two fractions, you multiply the first one by the multiplicative inverse of the second
5÷17=51×71=5×71×1=351=35
Multiply numerators together and denominators together.
25×37=2×35×7=635
Write the given equation
a+134=2
Subtract 134 from both sides of the equation
a+134−134=2−134
Simplify to obtain
a=2−134
Simplify the right side
=2−1−34
Simplify
1−34
Rewrite 1 as a fraction 44
=44−34=14
Hence
a=1/4
There are two whole shaded items above and one shaded at 34. Hence the mixed number
234 represents the shaded parts.
Let us say she worked n hour on Friday. The total (addition) for the 5 days is 15 hours. Let us add all hours for 5 days
312+4+216+112+n=15
Add whole numbers together and fractions together
(3+4+2+1)+(12+16+12)+n=15
Simplify the expressions within the brackets on the left side
10+(1+16)+n=15
Which also simplifies to
11+16+n=15
Subtract 11+16 from both sides of the above equation
11+16+n−11−16=15−11−16
Simplifies the left and the right sides to obtain
n=4−16
Rewrite 4 as a fraction with denominator 4
n=164−16
n=154
It is an improper fraction that can be written as a mixed number
n=154=12+34=334
Tina worked 3 and 34 hours on Friday.
Write 1710 in decimal form as follows
1710=1+7÷10=1+0.7=1.7 and corresponds to point W.
1.7 and corresponds to point W on the graph.
Write mixed number as a sum of a whole part and a fractional part
213=2+13
Write 2 as a fraction with denominator 3
=21×33+13
Simplify
=63+13
Add fractions with common denominator
=73
213 as an
213=73
Divide 31 by 8 to obtain a quotient equal to 3 and a remainder equal to 7 which can be written as
31=3×8+7
Hence we can write that
318=3×8+78=3×88+78
Simplify
=3+78=378
318 as a mixed number is equal to 378
3×14 may be written as
3×14=(1+1+1)×14
Use distribution
=14+14+14
314 is a mixed number with a whole part equal to 3 and a fractional part equal to 14 and is written as
314=3+14
Rewrite the two fractions with the same denominator. The same denominator is the lowest common multiple (LCM) of 5 and 8. First list the first few multiples of 5 and 8 until we obtain a common multiple
factors of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
factors of 8: 8, 16, 24, 32, 40, ...
The LCM of 5 and 8 is 40
Rewrite the two fractions with the same denominator 40 (which is the LCM)
25=25×88=1640
38=38×55=1540
1640 is greater than 1540 and therefore 25 is greater than 38 and therefore the above statement is true.
The fraction 76 has its numerator greater than its denominator and hence it is greater than 1.
The remaining 3 fractions 35,13 and 49 have their numerators smaller than their denominators and are therefore all less than 1. They can be compared by first writing them with the same denominator.
The same denominator may be the lowest common multiple of their denominators 5, 3 and 9.
factors of 5: 5, 10, 15, 25, 30, 35, 40, 45,...
factors of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,...
factors of 9: 9, 18, 27, 36, 45,...
The lowest common multiple of the denominators 5, 3 and 9 is 45. Hence we rewrite the three fractions with the common denominator 45 as follows:
35=35×99=2745
13=13×1515=1545
49=49×55=2045
Using the above fractions, we now order the given fractions from least to greatest as follows
13,49,35,76
23 of 4 is equal to:
23×4=23×41=2×43×1
Simplify
=83
Write 8 as 6 + 2. (6 is a multiple of 3)
=6+23
Rewrite as a sum of fractions
=63+23
Simplify
=2+23=223
Hence 23 of 4 as a mixed number is equal to
223
One hour is equal to 60 minutes. Hence 23 of an hour is equal to
23×60
Rewrite 60 as a fraction 601
=23×601
Multiply fractions and simplify
=2×603×1=1203
Rewrite fraction as a division and simplify
=120÷3=40 minutes
Conclusion: Hence 23 of an hour is equal to 40 minutes.
The large square is divided into 16 small squares. Hence every small square is 116 of the large square.
red: 4 small squares represent 4×116=416=14 of the large square
blue: 1 small square represents 1×116=116 of the large square
orange: half a small square represents 12 of 116 = 12×116=132 of the large square
green: 1 small square and 1/2 of a small square represents 116+12×116
Simplify
=116+132
Rewrite the fraction 116 with denominator 32
=116×22+132
Simplify
=332 of the large square
black: 3 small squares represent 3×116=316 of the large square
yellow: 3 small squares represent 3×116=316 of the large square
We can write the color with the corresponding fractions as follows:
red: 14 , blue: 116 , orange: 132 , green: 332 , black: 316 , yellow: 316
Fractions
Primary Maths (grades 4 and 5) with Free Questions and Problems With Answers
Middle School Maths (grades 6,7,8 and 9) with Free Questions and Problems With Answers