Calculator Comparing Fractions

Rules for expressions with fractions:

Fractions - Use a forward slash to separate the numerator and denominator. For example, for five-hundredths, enter 5/100.

Mixed numbers Leave one space between the whole number and the fraction part, and use a forward slash for the fraction. For example, enter 1 2/3 . For negative mixed numbers, write the negative sign before the whole number, such as -5 1/2.

Division of fractions - Since the forward slash is used for both fraction lines and division, use a colon (:) to divide fractions. For example, to divide 1/2 by 1/3, enter 1/2 : 1/3.

Decimals Enter decimal numbers using a decimal point (.), and they will be automatically converted to fractions. For example, enter 1.45.

Math Symbols

Symbol	Symbol name	Symbol Meaning	Example
+	plus sign	addition	1/2 + 1/3
-	minus sign	subtraction	1 1/2 - 2/3
*	asterisk	multiplication	2/3 * 3/4
×	times sign	multiplication	2/3 × 5/6
:	division sign	division	1/2 : 3
/	division slash	division	1/3 / 5
:	colon	complex fraction	1/2 : 1/3
^	caret	exponentiation / power	1/4^3
()	parentheses	calculate expression inside first	-3/5 - (-1/4)

Order of Operations

Ever wondered why calculators don't just work left to right? This calculator follows the mathematical order of operations — a set of rules that ensures everyone solves expressions the same way, every time.

Popular Memory Tricks

Different regions use different mnemonics to remember this order:

* PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
* BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
* BODMAS - Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction
* GEMDAS - Grouping symbols (parentheses, brackets, braces: (){}), Exponents, Multiplication, Division, Addition, Subtraction

The Golden Rules

Rule 1: Multiplication and division always come before addition and subtraction. Think of them as the VIPs that skip to the front of the line!

Rule 2: When operations have equal priority (like × and ÷, or + and −), work from left to right—just like reading a book.

Rule 3: Parentheses change the natural order of evaluation of operations.

Fractions in word problems:

• The numerator
  The numerator of the fraction is 5 more than its denominator. If 4 is added to the numerator and denominator, the fraction obtained is 6/5. What is that fraction?
• Conner
  Conner picked 8 1/5 pounds of apples. Louisa picked 9 2/3 pounds of apples. How many apples, more pounds, did Louisa pick than Conner?
• Fraction difference
  How much is 1/3 bigger than 1/9?
• Taylor
  Taylor filled eight 5 oz glasses of orange juice 2/3 full. Emeline filled five 9 oz glasses of orange juice 3/4 full. Who used more juice?
• Comparing by height
  Ira is 1 2/5 m tall. Her mother is 4/5 m as tall as Ira. How many times is Ira's mother taller than her?
• Quarter of 60 grams
  For a science experiment, students need to find 25% of 60 grams. John says, "I can find this by calculating 1/4 of 60." Andre says, "25% of 60 means 25/100 times 60." Do you agree with either of them? Show your reasoning.
• Dogs weights
  Four out of nine dogs weigh less than 20 pounds. What is the decimal equivalent for the number of dogs weighing less than 20 pounds?

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