Math  /  Numbers & Operations

Question13914647=13 \frac{9}{14}-6 \frac{4}{7}=

Studdy Solution

STEP 1

What is this asking? We're subtracting one mixed number from another, which means finding the difference between two numbers that have both whole number and fractional parts. Watch out! Remember to deal with the whole numbers and fractions separately, and watch out for needing to borrow from the whole number to subtract the fractions!

STEP 2

1. Convert to Improper Fractions
2. Find a Common Denominator
3. Subtract the Fractions
4. Subtract the Whole Numbers
5. Simplify

STEP 3

Alright, let's **kick things off** by converting these mixed numbers into improper fractions!
We do this because it's much easier to subtract fractions when they aren't attached to whole numbers.

STEP 4

First, we tackle 1391413 \frac{9}{14}.
Multiply the **whole number** (1313) by the **denominator** (1414): 1314=18213 \cdot 14 = 182.
This tells us how many fourteenths are in the whole number part.

STEP 5

Now, **add** that result (182182) to the **numerator** (99): 182+9=191182 + 9 = 191.
So, 1391413 \frac{9}{14} is the same as 19114\frac{191}{14}.
Awesome!

STEP 6

Next up: 6476 \frac{4}{7}.
Multiply the **whole number** (66) by the **denominator** (77): 67=426 \cdot 7 = 42.

STEP 7

Add that result (4242) to the **numerator** (44): 42+4=4642 + 4 = 46.
So, 6476 \frac{4}{7} becomes 467\frac{46}{7}.
Fantastic!

STEP 8

Now, to subtract these fractions, we need a **common denominator**.
We have 19114\frac{191}{14} and 467\frac{46}{7}.
Notice that 1414 is a multiple of 77: 72=147 \cdot 2 = 14.
So, our **common denominator** will be 1414!

STEP 9

We need to convert 467\frac{46}{7} to have a denominator of 1414.
We multiply both the numerator and the denominator by 22: 46722=46272=9214\frac{46}{7} \cdot \frac{2}{2} = \frac{46 \cdot 2}{7 \cdot 2} = \frac{92}{14}.
We're multiplying by 22\frac{2}{2}, which is just 11, so the value of the fraction doesn't change, just how we write it.

STEP 10

With our common denominator, we can **subtract** the fractions: 191149214=1919214=9914\frac{191}{14} - \frac{92}{14} = \frac{191 - 92}{14} = \frac{99}{14}.
We subtracted the numerators and kept the denominator the same.

STEP 11

Since we converted to improper fractions earlier, the whole numbers were already taken care of in the fraction subtraction!

STEP 12

Let's convert 9914\frac{99}{14} back to a mixed number.
How many times does 1414 go into 9999? 147=9814 \cdot 7 = 98, so 1414 goes into 9999 seven times with a remainder of 9998=199 - 98 = 1.
This gives us the mixed number 71147 \frac{1}{14}.

STEP 13

Our **final answer** is 71147 \frac{1}{14}!

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