Download Subtracting Fractions with the same Denominator

5th Grade Essential Skills Test
Study Guide
3rd Nine Weeks
M5.3.1 - Add and subtract fractions with like denominators; estimate using
fractions and decimals. (Textbook Chapter 10)
Adding Fractions with the same Denominator
Fractions consist of two numbers. The top number is called the numerator. The
bottom number is called the denominator.
numerator
denominator
To add two fractions with the same denominator, add the numerators and place
that sum over the common denominator.
Subtracting Fractions with the same Denominator
Fractions consist of two numbers. The top number is called the numerator. The
bottom number is called the denominator.
numerator
denominator
To subtract two fractions with the same denominator, subtract the numerators
and place that difference over the common denominator.
Adding Mixed Numbers with the same Denominator
Mixed numbers consist of an integer followed by a fraction.
How to add two mixed numbers whose fractions have the same
denominator:





Add the numerators of the two fractions
Place that sum over the common denominator.
If this fraction is improper (numerator larger than or equal to the
denominator) then convert it to a mixed number
Add the integer portions of the two mixed numbers
If adding the fractional parts created a mixed number then add its integer
portion to the sum.
Example: 3 2/3 + 5 2/3 =
Add the fractional part of the mixed numbers
2/3 + 2/3 = 4/3
Convert 4/3 to a mixed number
4/3 = 1 1/3
Add the integer portions of the mixed numbers 3 + 5 = 8
Add the integer from the sum of the fractions
8+1=9
State the final answer:
9 1/3
Subtracting Mixed Numbers with the Same Denominator
Mixed numbers consist of an integer followed by a fraction.
How to subtract mixed numbers having the same denominator:





Make the first numerator larger than the second if it is not.
Subtract the second numerator from the first
Place that difference over the common denominator.
Subtract the integer portions of the two mixed numbers
State the answer
Example: 5 1/3 - 3 2/3 =
Make the first numerator larger than the second
5 1/3 = 4 4/3
Subtract the fractional parts of the mixed numbers 4/3 - 2/3 = 2/3
Subtract the integer portions of the mixed numbers 4 - 3 = 1
State the final answer:
1 2/3
Estimate using fractions and decimals
Fractions – To estimate sums and differences, round each fraction or
mixed number to the nearest whole number, then add or subtract the rounded
numbers to get the estimate.
Example: ¾ + 1 ¾
¾ rounds to 1, 1 ¾ rounds to 2. Add 1+2 to get your estimate of 3.
*NOTE: Do NOT add or subtract the original numbers then round your
answer. That is NOT AN ESTIMATE!!!
Which way to round: Look at the numerator and denominator. If the
numerator is more than half of the denominator, round up. If not, round to the
last whole number.
Examples:
1 2/5 would round to 1 since 2 is less than half of 5
2 7/8 would round to 3 since 7 is more than half of 5
Decimals – To estimate sums or differences of decimals, round the
decimal to the nearest whole number, then add or subtract.
Example: Estimate the sum 4.32 + 5.98.
4.32 rounds to 4, 5.98 rounds to 6. 4 + 6 = 10. This is your estimate.
*NOTE: Do NOT add or subtract the original numbers then round your
answer. That is NOT AN ESTIMATE!!!
M5.3.2 - Compare and order fractions; write equivalent fractions. (Textbook
Chapter 9)
Compare and order fractions - If the denominators of two fractions are the
same, the fraction with the largest numerator is the larger fraction.
For example 5/8 is larger than 3/8 because all of the pieces are the same and
five pieces are more than three pieces.
If the numerators of two fractions are the same, the fraction with the smaller
denominator is the larger fraction.
For example 5/8 is larger than 5/16 because each fraction says there are five
pieces but if an object is divided into 8 pieces, each piece will be larger than if the
object were divided into 16 pieces. Therefore, five larger pieces are more than
five smaller pieces.
A decimal number and a fractional number can be compared. One number is
either greater than, less than or equal to the other number.
When comparing fractional numbers to decimal numbers, convert the fraction to
a decimal number by division and compare the decimal numbers.
To compare decimal numbers, start with tenths and then hundredths etc. If one
decimal has a higher number in the tenths place then it is larger and the decimal
with less tenths is smaller. If the tenths are equal compare the hundredths, then
the thousandths etc. until one decimal is larger or there are no more places to
compare.
Example: Which is greater, 0.45 or 0.410?
Compare the digits left to right until you come to one that is different. In the
example, the 0s are the same, the 4/10 are the same, but when you get to the
hundredths place, the 5 is greater than the 1. So,
0.45>0.410
Converting a Fraction to a Decimal
Do the following steps to convert a fraction to a decimal:
For example: Convert 4/9 to a decimal.


Divide the numerator of the fraction by the denominator (e.g. 4 ÷
9=0.44444)
Round the answer to the desired precision.
Write equivalent fractions – To write equivalent fractions, multiply or divide
both the numerator and denominator by the same number. If you divide, you
must use a common factor or greatest common factor (GCF – see below).
Example: Write an equivalent fraction for ¾.
3 2 6

4 2 8
Example: Write
9
in simplest form.
12
Factors of 9: 1, 3, 9
Factors of 12: 1, 2, 3, 4, 6, 12
93 3

12  3 4
GCF = 3
M5.3.3 - Find greatest common factor, least common multiple; use
divisibility rules (2,5,10,3,6,9) (Textbook Chapter 5 Lesson 5; Chapter 9)
Divisibility Rules
A number is divisible by
If
2
It ends in 0,2,4,6 or 8
3
The sum of the digits is divisible by 3
4
The last two digits form a number
divisible by 4 (or end in 00)
5
It ends in 5 or 0
6
It is divisible by BOTH 2 and 3
9
The sum of the digits is divisible by 9
10
It ends in 0
Greatest Common Factor – To find the Greatest Common Factor (GCF) of two
or more numbers, use divisibility rules to find factors of the numbers, list the
common ones and find the greatest.
Example: Find the GCF for 12 and 18
Factors of 12: 1,2,3,4,6,12
Factors of 18: 1,2,3,6,9,18
Common Factors: 1,2,3,6
Greatest Common Factor: 6
Least Common Multiple – The least common multiple (LCM) of two or more
numbers is the lowest number which is a multiple of all the numbers. To find the
multiples, multiply the number by 1, then 2, then 3 and so on (skip counting).
Example: Find the LCM for 4, 6 and 9
Multiples of 4: 4,8,12,16,20,24,28,32,36,40
Multiples of 6: 6,12,18,24,30,36,42,48,54,60
Multiples of 9: 9,18,27,36,45,54,63,72,81,90
The lowest number that is in all three lists is 36, so the LCM is 36.