Calculate without using a calculator
5 3/5÷ 7/10
First, convert 5 3/5 to an improper fraction:
5 3/5 = (5 x 5 + 3)/5 = 28/5
Then, convert 7/10 to an equivalent fraction with a denominator of 5:
7/10 = (7 x 1)/ (10 x 1) = 7/10 = 14/20 = 21/30
Now, we can rewrite the division expression as a multiplication expression by flipping the second fraction:
(28/5) x (30/21)
We can simplify this expression by canceling out factors that are common to both the numerator and the denominator. For example, 5 and 21 have a common factor of 5, which can be canceled out:
(28/1) x (6/3)
We can also simplify 28/1 to just 28:
28 x (6/3)
And finally, we can simplify 6/3 to just 2:
28 x 2 = 56
Therefore, 5 3/5 ÷ 7/10 = 56.
To calculate without a calculator, we can follow these steps:
Step 1: Convert the mixed number into an improper fraction:
5 3/5 = ((5 x 5) + 3)/5 = 28/5
Step 2: Invert the divisor (the second fraction) to find its reciprocal:
7/10 becomes 10/7
Step 3: Multiply the dividend (28/5) by the reciprocal of the divisor (10/7):
(28/5) x (10/7) = (28 x 10) / (5 x 7) = 280/35
Step 4: Simplify the fraction:
The numerator and denominator share a common factor of 7, so we can divide both by 7:
280/35 = (280 ÷ 7)/(35 ÷ 7) = 40/5
Step 5: Simplify the fraction further, if possible:
40/5 = (40 ÷ 5)/(5 ÷ 5) = 8/1 = 8
Therefore, 5 3/5 ÷ 7/10 = 8.