30/40 simplified in lowest terms provides the detailed information of what is the simplest form of 30/40, and the answer with steps help students to understand how to simplify the fraction in simplest form.
Simplify 30/40 in Lowest Terms 30/40 = (?)
30/40 = (2 x 3 x 5)/(2 x 2 x 2 x 5)
= 3/4 30/40 = 3/4The simplest form of 30/40 is 3/4
where,
30/40 is the given fraction to be simplified,3/4 is the lowest term of 30/40.
The below solution with step by step work shows how to find what is the lowest term of 30/40. The fraction 30/40 simplified can be found by using anyone of the below two methods: 1. Prime factorization method, 2. GCF method.
Prime Factorization Method :
step 1 Observe the input parameters and what to be found:
Input values: Fraction = 30/40
what to be found:
30/40 = ? Find what is the lowest term of 30/40.step 2 Find the prime factors of the numerator of given fraction 30/40.
Prime factors of 30 = 2 x 3 x 5
step 3 Find the prime factors of the denominator of given fraction 30/40.
Prime factors of 40 = 2 x 2 x 2 x 5
step 4 Rewrite the fraction 30/40 in the form of prime factors as like the below:
30/40= (2 x 3 x 5) / (2 x 2 x 2 x 5)
step 5 Check and cancel the factors of 30 and 40 if any factors in the numerator and denominator can be cancelled each other in the above fraction of prime factors:
= (2 x 3 x 5) / (2 x 2 x 2 x 5)
= ( 3 )/( 2 x 2 )
step 6 Simplify and rewrite the fraction as like the below:
= 3/4
30/40 = 3/4 Hence,
the simplest form of 30/40 is 3/4.
GCF Method :
step 1 Observe the input parameters and what to be found:
Input values: Fraction = 30/40
what to be found:
30/40 = ? Find what is the lowest term of 30/40.step 2 Find GCF (Greatest Common Factor) for both numerator and denominator of the fraction 30/40.
The GCF of 30 and 40 is 10.step 3 Divide the numerator and denominator of the fraction 30/40 by GCF 10:
= (30/10)(40/10)
step 4 Simplify the above expression:
= (30/10)(40/10)
= 3/4
30/40 = 3/4 Hence,
3/4 is the simplified or lowest term of 30/40.
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Math and Arithmetic
Find equivalent fractions. Enter a fraction, mixed number or integer to get fractions that are equivalent to your input. Example entries:
- Fraction - like 2/3 or 15/16
- Mixed number - like 1 1/2 or 4 5/6
- Integer - like 5 or 28
What are Equivalent Fractions?
Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.
For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100
How to Find Equivalent Fractions
Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.
Example Equivalent Fractions
Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number:
\( \dfrac{3}{4} \times \dfrac{2}{2} = \dfrac{6}{8} \)
\( \dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{9}{12} \)
\( \dfrac{3}{4} \times \dfrac{4}{4} = \dfrac{12}{16} \)
\( \dfrac{3}{4} \times \dfrac{5}{5} = \dfrac{15}{20} \)
\( \dfrac{3}{4} \times \dfrac{6}{6} = \dfrac{18}{24} \)
Therefore these are all equivalent fractions:
\( \dfrac{3}{4} = \dfrac{6}{8} = \dfrac{9}{12} = \dfrac{15}{20} = \dfrac{18}{24} \)
Note that if you reduce all of these fractions to lowest terms, they equal 3/4.
For additional fraction help see our Fractions Calculator, Simplify Fractions Calculator and Mixed Numbers Calculator.
The simplest form of 30/40 is 3/4.
Steps to simplifying fractions
- Find the GCD (or HCF) of numerator and denominator
GCD of 30 and 40 is 10 - Divide both the numerator and denominator by the GCD
30 ÷ 10/40 ÷ 10 - Reduced fraction: 3/4
Therefore, 30/40 simplified to lowest terms is 3/4.
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Equivalent fractions: 60/80 15/20 90/120 150/200 6/8 210/280
More fractions: 60/40 30/80 90/40 30/120 31/40 30/4129/40 30/39
Equivalent Fractions Calculator
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Here is the answer to questions like: 30/40 or What numbers are equivalent to 30/40?
This Equivalent Fractions Calculator will show you, step-by-step, equivalent fractions to any fraction you input.
See below the step-by-step solution on how to find equivalent fractions.
Two fractions are equivalent when they are both equal when written in lowest terms. The fraction 6080 is equal to 34 when reduced to lowest terms. To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction (34) by the same natural number, ie, multiply by 2, 3, 4, 5, 6 ...
Important: 3040 looks like a fraction, but it is actually an improper fraction.
- 68 is equivalent to 3040 because 3 × 24 × 2 = 68
- 912 is equivalent to 3040 because 3 × 34 × 3 = 912
- 1216 is equivalent to 3040 because 3 × 44 × 4 = 1216
- 1520 is equivalent to 3040 because 3 × 54 × 5 = 1520
- and so on ...
At a glance, equivalent fractions look different, but if you reduce then to the lowest terms you will get the same value showing that they are equivalent. If a given fraction is not reduced to lowest terms, you can find other equivalent fractions by dividing both numerator and denominator by the same number.
Finding equivalent fractions can be ease if you use this rule:
Equivalent fractions definition: two fractions ab and cd are equivalent only if the product (multiplication) of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.
In other words, if you cross-multiply (ab and cd) the equality will remain, i.e, a.d = b.c. So, here are some examples:
- 34 is equivalent to 3040 because 3 × 40 = 4 × 30 = 120
- 68 is equivalent to 3040 because 6 × 40 = 8 × 30 = 240
- 912 is equivalent to 3040 because 9 × 40 = 12 × 30 = 360
- 1216 is equivalent to 3040 because 12 × 40 = 16 × 30 = 480
This Equivalent Fractions Table/Chart contains common practical fractions. You can easily convert from fraction to decimal, as well as, from fractions of inches to millimeters.
| 1/64 | 0.015625 | 0.397 | |||||
| 2/64 | 1/32 | 0.03125 | 0.794 | ||||
| 3/64 | 0.046875 | 1.191 | |||||
| 4/64 | 2/32 | 1/16 | 0.0625 | 1.588 | |||
| 5/64 | 0.078125 | 1.984 | |||||
| 6/64 | 3/32 | 0.09375 | 2.381 | ||||
| 7/64 | 0.109375 | 2.778 | |||||
| 8/64 | 4/32 | 2/16 | 1/8 | 0.125 | 3.175 | ||
| 9/64 | 0.140625 | 3.572 | |||||
| 10/64 | 5/32 | 0.15625 | 3.969 | ||||
| 11/64 | 0.171875 | 4.366 | |||||
| 12/64 | 6/32 | 3/16 | 0.1875 | 4.763 | |||
| 13/64 | 0.203125 | 5.159 | |||||
| 14/64 | 7/32 | 0.21875 | 5.556 | ||||
| 15/64 | 0.234375 | 5.953 | |||||
| 16/64 | 8/32 | 4/16 | 2/8 | 1/4 | 0.25 | 6.35 | |
| 17/64 | 0.265625 | 6.747 | |||||
| 18/64 | 9/32 | 0.28125 | 7.144 | ||||
| 19/64 | 0.296875 | 7.541 | |||||
| 20/64 | 10/32 | 5/16 | 0.3125 | 7.938 | |||
| 21/64 | 0.328125 | 8.334 | |||||
| 22/64 | 11/32 | 0.34375 | 8.731 | ||||
| 23/64 | 0.359375 | 9.128 | |||||
| 24/64 | 12/32 | 6/16 | 3/8 | 0.375 | 9.525 | ||
| 25/64 | 0.390625 | 9.922 | |||||
| 26/64 | 13/32 | 0.40625 | 10.319 | ||||
| 27/64 | 0.421875 | 10.716 | |||||
| 28/64 | 14/32 | 7/16 | 0.4375 | 11.113 | |||
| 29/64 | 0.453125 | 11.509 | |||||
| 30/64 | 15/32 | 0.46875 | 11.906 | ||||
| 31/64 | 0.484375 | 12.303 | |||||
| 32/64 | 16/32 | 8/16 | 4/8 | 2/4 | 1/2 | 0.5 | 12.7 |
| 33/64 | 0.515625 | 13.097 | |||||
| 34/64 | 17/32 | 0.53125 | 13.494 | ||||
| 35/64 | 0.546875 | 13.891 | |||||
| 36/64 | 18/32 | 9/16 | 0.5625 | 14.288 | |||
| 37/64 | 0.578125 | 14.684 | |||||
| 38/64 | 19/32 | 0.59375 | 15.081 | ||||
| 39/64 | 0.609375 | 15.478 | |||||
| 40/64 | 20/32 | 10/16 | 5/8 | 0.625 | 15.875 | ||
| 41/64 | 0.640625 | 16.272 | |||||
| 42/64 | 21/32 | 0.65625 | 16.669 | ||||
| 43/64 | 0.671875 | 17.066 | |||||
| 44/64 | 22/32 | 11/16 | 0.6875 | 17.463 | |||
| 45/64 | 0.703125 | 17.859 | |||||
| 46/64 | 23/32 | 0.71875 | 18.256 | ||||
| 47/64 | 0.734375 | 18.653 | |||||
| 48/64 | 24/32 | 12/16 | 6/8 | 3/4 | 0.75 | 19.05 | |
| 49/64 | 0.765625 | 19.447 | |||||
| 50/64 | 25/32 | 0.78125 | 19.844 | ||||
| 51/64 | 0.796875 | 20.241 | |||||
| 52/64 | 26/32 | 13/16 | 0.8125 | 20.638 | |||
| 53/64 | 0.828125 | 21.034 | |||||
| 54/64 | 27/32 | 0.84375 | 21.431 | ||||
| 55/64 | 0.859375 | 21.828 | |||||
| 56/64 | 28/32 | 14/16 | 7/8 | 0.875 | 22.225 | ||
| 57/64 | 0.890625 | 22.622 | |||||
| 58/64 | 29/32 | 0.90625 | 23.019 | ||||
| 59/64 | 0.921875 | 23.416 | |||||
| 60/64 | 30/32 | 15/16 | 0.9375 | 23.813 | |||
| 61/64 | 0.953125 | 24.209 | |||||
| 62/64 | 31/32 | 0.96875 | 24.606 | ||||
| 63/64 | 0.984375 | 25.003 | |||||
| 64/64 | 32/32 | 16/16 | 8/8 | 4/4 | 2/2 | 1 | 25.4 |
Reference:
- [1] How to Find Equivalent Fractions
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