#### Solved Examples and Worksheet for Problems on Equivalent Fractions with Denominators 10 and 100

Q1What is the equivalent fraction of 610 = ?100, and use this relation to add 610 + 6100?
A. 60100; 66100
B. 60100; 12100
C. 6100; 12100
D. 60100; 36100

Step: 1
610 = ?100
[Given.]
Step: 2
As the denominators are multiples of 10, multiply both the numerator and denominator of the fraction 610 by 10.
Step: 3
610 × 1010 = 60100
[Multiply.]
Step: 4
Now, solve 610 + 6100.
Step: 5
= 60100 + 6100
[From step 3.]
Step: 6
= 66100
Step: 7
Therefore, '60100' is the equivalent fraction of 610 and '66100' is the sum of 610 + 6100.
Correct Answer is :   60100; 66100
Q2Steve has 310 inch ribbon and Mark has 87100 inch ribbon. If the 2 friends decide to join the 2 ribbons, find the total length of the ribbon.

A. 90100 inches
B. 117100 inches
C. 107100 inches
D. 171100 inches

Step: 1
Length of ribbon Steve has = 310 inches
Length of ribbon Mark has = 87100 inches
Step: 2
Adding the lengths of both the ribbons
310 + 87100
Step: 3
Since denominators are different and as they are multiples of 10, we use 310 = 30100
Therefore 30100 + 87100 = 117100
Correct Answer is :   117100 inches
Q3Evelyn walked 310 of a mile yesterday and 31100 of a mile today. How many miles has Evelyn walked in these 2 days. Also identify the equivalent fractional relation used in addition.

A. 33100
B. 6110
C. 3310
D. 61100

Step: 1
Miles walked by Evelyn yesterday = 310
Miles walked by Evelyn today = 310
Step: 2
Total miles walked by Evelyn in 2 days = 310 + 31100
Step: 3
We observe that the denominators of the fractions are not equal, but are multiples of 10.
So we multiply 310 with 10, both numerator and denominator so as to make the denominators same/ alike
Step: 4
Numerator 3 × 10 = 30 and Denominator 10 × 10 = 100
Step: 5
Thus 310 = 30100
Step: 6
Now adding by substituting equivalent fractional relationship 310 = 30100
3100 + 31100 = 30100 + 31100 = 61100
Q4Dennis bought 85100 gallons of paint. If Dennis already have 910 gallons of paint. How much paint Dennis have altogether?

A. 94100
B. 175100
C. 859100
D. 9410

Step: 1
Gallons of paint already with Dennis = 910
Gallons of paint bought by Dennis = 85100
Step: 2
We observe that the denominators of the fractions are not equal, but are multiples of 10.
So we multiply 910with 10, both numerator and denominator so as to make the denominators same/alike.
Step: 3
Thus, an equivalent fraction of 910 is 90100
[Multiply both the numerator and denominator of910 with 10]
Step: 4
Adding 85100 and 910, 910 + 85100 = 90100 + 85100
[Use an equivalent fraction of 910 = 90100]
Step: 5
we get 90100 + 85100 = 175100
[Add numerators as denominators are same]
Q5Eight pens out of a packet of 10 pens are in blue color. It was observed that there are 78 pens out of 100 pens are in blue color. How many pens is blue color in all?

A. 158100 blue color pens
B. 788100 blue color pens
C. 8610 blue color pens
D. 86100 blue color pens

Step: 1
The number of blue pens out of ten pens = 810
Step: 2
The number of blue pens out of hundred pens = 78100
Step: 3
We observe that the denominators of the fractions are not equal, but are multiples of 10. So we multiply 810 with 10, both numerator and denominator so as to make the denominators same/alike.
Step: 4
Thus, an equivalent fraction of 810 is 80100 .
[Multiply both the numerator and denominator of 810 with 10]
Step: 5
810 + 78100 =80100 + 78100
[Use an equivalent fraction of 810 = 80100]
Step: 6
We get 80100 + 78100 = 158100
[Add numerators as denominators are same]
Correct Answer is :   158100 blue color pens
Q6Find the equivalent fraction of 6910 and add 6910 and 33100.
A. 690100, 102100
B. 69100, 102100
C. 69100, 723100
D. 690100, 723100

Step: 1
We see that the denominators are not same and that the denominators are multiples of 10.
Step: 2
Take the highest denominator i.e. 100, and consider the lowest denominator 10
Step: 3
So, an equivalent fraction of 6910 is 690100
[Multiply both the numerator and denominator of 6910]
Step: 4
Adding 6910 and 33100, 6910 + 33100 = 690100 + 33100
[Use an equivalent fraction of 6910 = 690100].
Step: 5
we get, 690100 + 33100 = 723100
[Add numerator as denominator are same]
Correct Answer is :   690100, 723100
Q7Identify the expression which has the answer 119100 if equivalent of 1110 = 110100
A. 1110 + 1810
B. 1910 + 1110
C. 1110 + 9100
D. 1910 + 810

Step: 1
Adding the option 1110 + 1810 = 2910
[Add numerators as denominators are same]
Step: 2
Adding the option 1910 + 1110 = 3010
[Add numerators as denominators are same]
Step: 3
Adding the option 1910 + 810 = 2710
[Add numerators as denominators are same]
Step: 4
Adding the option 1110 + 9100 = 110100 + 9100
[Use an equivalent fraction of 1110 = 110100.]
Step: 5
we get 110100 + 9100 = 119100
[Add numerators as denominators are same]
Correct Answer is :   1110 + 9100
Q8Add 210 and 11100 by finding the equivalent fraction of 210.
A. 20100 and 31100
B. 2100 and 32100
C. 2010 and 30100
D. 20100 and 21100

Step: 1
The given fractions are 210 and 11100.
Step: 2
Here the denominators are 10 and 100. These denominators are different.
Step: 3
Before adding and subtracting fractions, the fractions should have equal denominators.
Step: 4
Take the LCD of the denominators 10 and 100. The LCD is 100.
Step: 5
: Now multiply both the numerators and denominators of the fractions 210 by 10 and 11100 by 1 to make the common denominator.
Step: 6
210 = 210 × 1010 = 2 × 1010 × 10 = 20100. Here 210 is equivalent to the fraction 20100.
Step: 7
11100 = 11100 × 11 = 11 × 1100 × 1 = 11100.
Step: 8
Now adding the two fractions 20100 and 11100
20100 + 11100.
Step: 9
Here denominators are common. So add the numerators directly.
Step: 10
20 + 11100 = 31100.
Correct Answer is :   20100 and 31100
Q9Add 910 and 90100 by finding the equivalent fraction of 910.

A. 900100 and 160100
B. 910 and 170100
C. 9010 and 180100
D. 90100 and 180100

Step: 1
The given fractions are 910 and 90100.
Step: 2
Here the denominators are 10 and 100. These denominators are different.
Step: 3
Before adding and subtracting fractions, the fractions should have equal denominators.
Step: 4
Take the LCD of the denominators 10 and 100. The LCD is 100.
Step: 5
Now multiply both the numerators and denominators of the fractions 910 by 10 and 90100 by 1 to make the common denominator.
Step: 6
910 = 910 × 1010 = 9 × 1010 × 10 = 90100. Here 910 is equivalent to the fraction 90100.
Step: 7
90100 = 90100 × 11 = 90 × 1100 × 1 = 90100.
Step: 8
Now adding the two fractions 90100 and 90100
90100 + 90100.
Step: 9
Here denominators are common. So add the numerators directly.
Step: 10
90 + 90100 = 180100.
Correct Answer is :   90100 and 180100
Q10What is the equivalent fraction of 810 = ?100 ? Use this relation to add 810 + 8100.

A. 80100 and 88100
B. 800100 and 88100
C. 8010 and 8810
D. 8100 and 86100

Step: 1
Given that 810 = ?100. Here we must find the unknown numerator to get the equivalent fraction for 810.
Step: 2
As the denominators are multiples of 10, multiply both numerator and denominator of the fraction 810 by 10 to get the equivalent fraction for 810.
Step: 3
810 = 810 × 1010 = 8 × 1010 × 10 = 80100.
Step: 4
: Here the equivalent fraction for 810 is 80100. So, the unknown numerator is 80.
Step: 5
Now we need to add the fractions 810 and 8100
810 + 8100 = 80100 + 8100
[80100 is equivalent to 810 from step 3.]
Step: 6
Here, the denominators are common. So add the numerators directly.
Step: 7
80 + 8100 = 88100.
Correct Answer is :   80100 and 88100
Q11What is the equivalent fraction of 3310 = ?100? Use this relation to add 3310 + 69100.

A. 33100 and 399100
B. 3300100 and 399100
C. 330100 and 399100
D. 333100 and 399100

Step: 1
Given that 3310 = ?100. Here we must find the unknown numerator to get the equivalent fraction for 3310.
Step: 2
As the denominators are multiples of 10, multiply both numerator and denominator of the fraction 3310 by 10 to get the equivalent fraction for 3310.
Step: 3
3310 = 3310 × 1010 = 33 × 1010 × 10 = 330100.
Step: 4
Here the equivalent fraction for 3310 is 330100. So, the unknown numerator is 330.
Step: 5
Now we need to add the fractions 3310 and 69100
3310 + 69100 = 330100 + 69100
[330100 is equivalent to 3310 from step 3.]
Step: 6
Here, the denominators are common. So add the numerators directly.
Step: 7
330 + 69100 = 399100.
Correct Answer is :   330100 and 399100
Q12What is the equivalent fraction of 9910 = ?100? Use this relation to add 9910 + 10100.

A. 9910 and 1000100
B. 99100 and 1000100
C. 990100 and 1000100
D. 9900100 and 1000100

Step: 1
Given that 9910 = ?100. Here we must find the unknown numerator to get the equivalent fraction for 9910.
Step: 2
As the denominators are multiples of 10, multiply both numerator and denominator of the fraction 9910 by 10 to get the equivalent fraction for 9910.
Step: 3
9910 = 9910 × 1010 = 99 × 1010 × 10 = 990100.
Step: 4
Here the equivalent fraction for 9910 is 990100. So, the unknown numerator is 990.
Step: 5
Now we need to add the fractions 9910 and 10100
9910 + 10100 = 990100 + 10100
[990100 is equivalent to 9910 from step 3.]
Step: 6
Here, the denominators are common. So add the numerators directly.
Step: 7
990 + 10100 = 1000100.
Correct Answer is :   990100 and 1000100