How To Calculate: 9 - 5³, 7/8 - 2⁵, And 6 7/12 - 3 1/3
Hey guys! Today, we're diving into some basic math calculations. We'll break down how to solve these expressions step by step, making it super easy to follow along. Whether you're brushing up on your math skills or tackling homework, this guide is for you. Let's jump right in!
1) Calculate 9 - 5³
When you're faced with an expression like 9 - 5³, it's essential to follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). In our case, the exponent comes first.
Step 1: Evaluate the Exponent
The expression 5³ means 5 raised to the power of 3, which is 5 * 5 * 5. Let's calculate it:
5 * 5 = 25
25 * 5 = 125
So, 5³ = 125.
Step 2: Perform the Subtraction
Now that we've calculated the exponent, we can substitute it back into our original expression:
9 - 5³ = 9 - 125
Subtracting 125 from 9 gives us:
9 - 125 = -116
Therefore, 9 - 5³ = -116.
Why is Order of Operations Important?
Following the order of operations is crucial because it ensures we all get the same answer. Imagine if we subtracted first: 9 - 5 = 4, and then cubed the result, 4³ = 64. That’s a completely different answer! Sticking to PEMDAS/BODMAS helps us maintain consistency in math.
Common Mistakes to Avoid
A common mistake is to subtract before evaluating the exponent. Always remember exponents come before subtraction. Another mistake is miscalculating the exponent itself. Take your time and double-check your multiplication to ensure accuracy.
2) Calculate 7/8 - 2⁵
Now, let's tackle our second expression: 7/8 - 2⁵. Again, we need to follow the order of operations, so exponents come before subtraction.
Step 1: Evaluate the Exponent
The expression 2⁵ means 2 raised to the power of 5, which is 2 * 2 * 2 * 2 * 2. Let's break it down:
2 * 2 = 4
4 * 2 = 8
8 * 2 = 16
16 * 2 = 32
So, 2⁵ = 32.
Step 2: Rewrite the Expression
Substitute the value of 2⁵ back into the original expression:
7/8 - 2⁵ = 7/8 - 32
Step 3: Perform the Subtraction
To subtract a whole number from a fraction, we need a common denominator. We'll convert 32 into a fraction with a denominator of 8.
32 = 32/1
Multiply both the numerator and denominator by 8:
32/1 * (8/8) = 256/8
Now, we can subtract:
7/8 - 256/8 = (7 - 256)/8 = -249/8
So, 7/8 - 2⁵ = -249/8.
Converting to a Mixed Number (Optional)
If you prefer, you can convert the improper fraction -249/8 into a mixed number. Divide 249 by 8:
249 ÷ 8 = 31 with a remainder of 1
So, -249/8 = -31 1/8.
Key Takeaways
The most important thing here is to remember the order of operations. Exponents before subtraction! Also, when subtracting fractions, make sure you have a common denominator. This makes the process much smoother and prevents errors.
3) Calculate 6 7/12 - 3 1/3
Our final expression is 6 7/12 - 3 1/3. This involves subtracting mixed numbers, which requires a few steps, but don't worry, we'll break it down.
Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions. To do this, multiply the whole number by the denominator and add the numerator, then put the result over the original denominator.
For 6 7/12:
(6 * 12) + 7 = 72 + 7 = 79
So, 6 7/12 = 79/12.
For 3 1/3:
(3 * 3) + 1 = 9 + 1 = 10
So, 3 1/3 = 10/3.
Step 2: Rewrite the Expression
Now, our expression looks like this:
79/12 - 10/3
Step 3: Find a Common Denominator
To subtract the fractions, we need a common denominator. The least common multiple of 12 and 3 is 12. So, we'll convert 10/3 to an equivalent fraction with a denominator of 12.
Multiply both the numerator and denominator of 10/3 by 4:
10/3 * (4/4) = 40/12
Step 4: Perform the Subtraction
Now we can subtract:
79/12 - 40/12 = (79 - 40)/12 = 39/12
So, 6 7/12 - 3 1/3 = 39/12.
Step 5: Simplify the Fraction (Optional)
The fraction 39/12 can be simplified. Both 39 and 12 are divisible by 3.
39 ÷ 3 = 13
12 ÷ 3 = 4
So, 39/12 = 13/4.
Step 6: Convert to a Mixed Number (Optional)
If you want, you can convert the improper fraction 13/4 back into a mixed number. Divide 13 by 4:
13 ÷ 4 = 3 with a remainder of 1
So, 13/4 = 3 1/4.
Tips for Subtracting Mixed Numbers
The trickiest part is usually finding the common denominator and converting mixed numbers to improper fractions. Take your time with these steps, and double-check your work. It’s also a good idea to simplify your fraction at the end if possible.
Final Thoughts
Alright, guys, we've walked through three different types of calculations! Remember the order of operations, and don't rush through the steps. Math might seem intimidating at first, but with practice, you'll become a pro. Keep practicing, and you'll master these skills in no time! Keep an eye out for more math guides coming soon!