how do i solve this math problem 4 2/5 * 1 1/4 - 1 3/5 / 1 1/2

Question

how do i solve this math problem 4 2/5 * 1 1/4 - 1 3/5 / 1 1/2

Answer 1

4 2/5 * 1 1/4 - 13/5 / 1 1/2:

The mixed number, 4 2/5, equals 22/5; the mixed number, 1 1/4 equals 5/4; and 1 1/2 equals 3/2

We now multiply 4 2/5 * 1 1/4 = 22/5 * 5/4 = (22 * 5)/(5 * 4) = 110/20 = 11/2.

Next, we evaluate the expression
(13/5) / (3/2) = 13/5 ÷ 3/2 = 13/5 x 2/3 = (13 x 2)/(5 x 3) = 26/15
Remember: dividing by a fraction means to multiply by its reciprocal.

Then, we subtract 11/2 – 26/15

One will see that Multiplication and Division have Precedence to Addition and Subtraction.

When evaluating arithmetic expressions, remember, "Please Excuse My Dear Aunt Sally." From this, we extract the first letter of each word: PEMDAS. This acronym helps us to remember the order of priority in arithmetic operations. We then have the priorities spelled-out: Parenthetic ...{..[...(...)...]..}... - Exponential - Multiplication - Division - Addition - Subtraction. For more info, consult your teacher or text; or, conduct research on this topic.

 

Then, it will become evident why it is not proper to subtract

4 2/5 * 1 1/4 - 13/5! It is because we had a division to perform before the subtraction.

Recall that we have the subtraction to perform:
11/2 - 26/15

From this, we have 30 as the least common denominator, since 2 and 15 have nothing in common. Take the 2 in the 11/2, and divide into 30 (equals 15). Then, multiply the 15 by 11 (equals 165). Next, take the 15 in 26/15, and divide into 30 (equals 2), then multiply the 2 by 26 (equals 52).

We finally have (165 - 52)/30 = 113/30

 

113/30 should be the preferred answer, but some teachers do ask for the mixed-number equivalent.

 

Answer 2

Okay, so you have to know three things in order - (1)how to determine the order of operations, (2) how to multiply and divide fractions, and simplify the results (3) and how to combine unlike fractions.  

 

You always do parenthesis first, then the multiplying and dividing, then the addition and subtraction.

 

So, let's add parens in the equation where they belong - 

 

(4 2/5 * 1 1/4) - (13/5 / 1 1/2)

 

Second, for simplicity, we'll put everything into improper fractions instead of letting the compound fractions distract us.

 

4 2/5 = 22/5

1 1/4 = 5/4

13/5 = 13/5

1 1/2 = 3/2

 

Giving us

 

(22/5 * 5/4) - (13/5 / 3/2)

 

Now to multiply and divide. Remember that when you're multiplying numerators and denominators, you can cross off any factors that are the same on the top and bottom.  In the left parens, we can kill the 5's and another factor of 2 (that's in both 22 and 4).  In the right parens, remember that dividing by a fraction is the same as multiplying by the flip of the fraction (so 13/5 / 3/2 is the same as 13/5 * 2/3).  

 

Thus, our four-term initial equation has resolved to two terms

 

(11/2) - (26/15)

 

Next, we have to add those terms together, which means they have to have the same factor on the bottom, before we add/subtract the top.  

 

Remember that you can multiple any number by 1 and it stays the same.  Any number, divided by itself, is 1, so we can multiply the top and bottom of these fractions by the same number, and we haven't changed the equation.  

 

We'll multiply the top and bottom of the left term by 15, and the top and bottom of the right term by 2, so that the bottoms of both terms are 30.

 

= (11*15/2*15) - (26*2/15*2)

 

= 165/30 - 52/30 

 

And then we subtract -

 

= 113/30

 

Now, we reduce the result if we can.  The three prime factors of 30 are 2, 3 and 5.  113 is not evenly divisible by any of these, so we'[re done in terms of reduction.

 

Your initial problem was presented in compound fractions, so we'll present the result the same way.  30 goes into 113 3 times, taking away 90, leaving a remainder of 23.

 

The answer is 

 

=3 23/30

 

And finally, we do a gut check.  Looking at the original problem, with (4 2/5 * 1 1/4) we were multiplying something over 4 by 1-1/4, so our intermediate number was a little over 5, and then taking away (13/5 / 1 1/2)  which is going to be something about 2 and a half that is reduced by a third, ending up under 2.  

 

The answer is over 3, so it matches the general answer we're expecting.

 

Voila!